Brobst can't stop with just one story because every person and place that comes to mind reminds him of another person or place from a century of living.
Brobst, who turned 104 on Sept. 2, begins by reminiscing about his birthplace -- Reading, Pa.
A keen observer might guess Brobst's background based on his slight Yankee accent and the print of a pagoda on his wall.
Reading is famous for its five-story red and gold pagoda, which sits almost 900 feet above the city on Mount Penn. The structure was built in 1908 -- two years after Brobst was born.
When asked about his siblings, Brobst thinks first of his own children: daughter, P.J. Magik; and son, John, who died in an automobile accident when he was 27 years old.
"He loved music, and I really think he would be a professional pianist if he had lived," Brobst said.
Brobst has one sister, Elizabeth Weber, who will be 100 in January.
Today, Brobst speaks of the places from his past as if they are still right outside his front door. His thoughts turn from Maiden Creek, where he spent most of his summers; to the Schuylkill River, which he remembers being black with soot because coal was washed in it; and then to Penn Street, which was planned with the rest of Reading by William Penn's two sons.
Brobst was raised in a large 12-room house on a corner street. The lights in the home ran on gas. While the family was playing cards, someone would have to put a quarter in a meter occasionally to keep the lights burning.
The technology available in homes across America changed rapidly while Brobst was a boy. He only had to look out his window to see how an invention of the mid-19th century had been put to use during his childhood.
The lights on the pagoda in Reading used to flash Morse Code to direct firemen and inform the public of everything from fundraising campaigns to World Series results.
Brobst's fascination with electricity led him to become interested in radio while it was still in its experimental stage.
He made a career out of repairing radios and later learned about televisions as well. He admits that the digital age, which has revolutionized modern television, has passed him by.
"I'm lost. Now my daughter is a lot more familiar with it than I," Brobst said.
Brobst's first car was a Maxwell. He still likes to brag that it was the same kind as comedian Jack Benny's chauffeur, Eddie "Rochester" Anderson.
When Brobst was 29, he married the love of his life, LaRue. The two were married for 66 years. They moved to Alabama in retirement to live on her family land, which he still calls home.
LaRue Brobst developed a fever on Easter in 1999. Later, she lost all her strength and fell to the floor while he was trying to help her up from her favorite chair.
"That was the last time that she called me by the name of 'Addison,'" Brobst said with a hint of sadness in his voice.
LaRue Brobst was moved to a nursing home for the rest of her life. She called her husband "Pop Pop" every time he visited until her death in 2001.
Although Brobst will never replace his beloved wife, he has made quite a few female friends since becoming a widower.
"I seem to have more girlfriends now than I did in my earlier days," he jokes.
Brobst celebrated his 104th birthday this year with a dinner at Ruby Tuesday's. He eats out almost every day because taste and smell are two senses that have not failed him yet.
He insists that his vital organs are working as well as can be considering that "they're as old as I am."
Brobst has never had a major health problem such as a heart attack or stroke. He has only been admitted to the hospital twice in his life. His first stay was when he was 98.
At one doctor visit, he answered truthfully with a "no" to a long list of problems on a health history until the nurse came to the question of alcohol consumption.
"She looked me right in the eye and said, 'If you answer yes to this question, I'm going to start drinking,'" Brobst said.
Brobst said he does sometimes drink a little before bed to help him sleep.
He has now lived so long that he was recently asked to prove he wasn't dead.
Someone from the local Social Security office called his home and asked to see him to verify that he was still alive at 104.
Brobst, who said he was bashful in his younger years, has now learned to have more fun.
When he emerged from his interview at the Social Security office, he told the man at the desk, "Everything went all right. They invited me back in 10 years."