Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering.
Add 1 pound sliced pre-cooked andouille sausage; cook 5–7 minutes, flipping occasionally, until browned and crispy at the edges. Remove sausage and set aside, leaving rendered fat in the pan.
Add 1 large yellow onion (chopped) and 2 bell peppers (cut into 1-inch pieces); cook over medium heat 8–10 minutes, stirring occasionally, until onion is translucent and peppers are tender-crisp.
Stir in 2 cloves minced garlic; cook 1 minute until fragrant.
Pour in 1 (14.5-ounce) can diced tomatoes (undrained) and 0.5 cup chicken broth. Add 1 teaspoon Cajun or Creole seasoning, 0.5 teaspoon salt, and 0.25 teaspoon black pepper. Bring to a gentle simmer, scraping up browned bits from the pan.
Return browned sausage to the skillet; stir to combine and simmer 5–7 minutes more until flavors meld and sauce thickens slightly.