Pat chicken dry; season both sides with salt and pepper.
Heat olive oil in a 4.5-quart pot over medium-high heat until shimmering.
Sear chicken 3 minutes per side until golden; transfer to a plate and rest 10 minutes, then dice or shred.
Melt butter in the same pot over medium heat, scraping up browned bits, about 1 minute.
Add onion, carrots, and celery; cook 5 minutes until softened.
Stir in garlic, hot sauce, Worcestershire, parsley, basil, oregano, mustard powder, and pepper; cook 30 seconds.
Pour in chicken broth and bring to a boil over medium-high heat.
Reduce heat to medium-low; return chicken and any juices to the pot. Simmer uncovered 15 minutes.
Add frozen mixed vegetables; partially cover and simmer 10-15 minutes until tender.
Taste and adjust salt and pepper. Ladle into bowls and serve warm.