Slice peppers into 1/2-inch strips and onion into half-moons; mince garlic. Do not prick the sausage.
Heat olive oil in a large skillet or cast-iron pan over medium-high heat until shimmering. Sear sausage links 8-10 minutes, turning every 2 minutes, until browned and cooked to 160F internal. Transfer to a plate; leave the rendered fat in the pan.
Reduce heat to medium. Add peppers and onion; cook 6-8 minutes, stirring occasionally, until softened with charred edges.
Clear the pan center; add garlic and red pepper flakes (if using). Stir 30 seconds until fragrant, then mix into the vegetables.
Pour in chicken broth and scrape up the browned bits. Simmer about 1 minute until slightly reduced.
Slice sausage into 1-inch pieces on the bias (or leave whole for sandwiches). Return to the pan, sprinkle with oregano, and toss. Simmer 1-2 minutes until heated through. Taste and adjust salt and pepper.