The West Philadelphia native's show takes a humorous look at the inner-workings of a Philadelphia school.
She named the fictitious Philly school (and the show) after her 6th-grade teacher, Ms. Joyce Abbott.
On Tuesday's "Jimmy Kimmel Live!," Kimmel surprised Brunson by bringing Ms. Abbott onto the show.
"The last time I saw Ms. Abbott was probably sixth grade," Brunson told Kimmel just before her former teacher appeared virtually on screen.
Once the teacher popped up, Brunson became emotional.
"I'm so proud of you," a joyful Ms. Abbott told her former student.
Kimmel asked the teacher how she found out the show was named after her.
"It was confirmed one night when I was watching 6abc news," Ms. Abbott said. "They were talking about the 'Abbott Elementary' show shortly after the pilot. The newscaster said, 'Ms. Abbott, if you're watching, Quinta would like to reconnect with you.' I was like 'Oh my God!'"
That newscaster was our very own Alicia Vitarelli!
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Brunson told Alicia that not only is the school named for Ms. Abbott, but also for actor Will Smith.
"My 6th-grade teacher was Miss Abbott, and she was a fantastic teacher in my life," Brunson told 6abc. "I made the first name of the school Willard because that's Will Smith's real name, and I just thought it would be funny to name it 'Willard Abbott Elementary.' A little nod to West Philadelphia."
On "Jimmy Kimmel Live!" Ms. Abbott called Brunson an awesome student who was shy at first.
"As I challenge all of my students, we have to speak in complete sentences. I build their confidence that whatever you want at life you can do it. You have to work hard," Ms. Abbott said. "We did projects where we worked hard to go to fabulous places - just instilling that in them, instilling their confidence.
Quinta was an awesome student, very driven at that time. She grew out of her shell. She was really our class spokesperson."
As Ms. Abbott spoke, Brunson wiped away tears from her face with tissues.
Ms. Abbott who is nearing 30 years of teaching said she is now ready for retirement.
"It's about time for me to retire," the educator told Kimmel.
To celebrate her retirement, Kimmel surprised Ms. Abbott with an all-expense paid first class, five-day trip for two.
Brunson shouted, "Oh my God, Ms. Abbott," as the teacher cheered in excitement.
"Abbott Elementary" airs Tuesday nights on 6abc.