Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.

Place chicken thighs and sausage links on the baking sheet. Season chicken lightly with salt and pepper.

Bake in the preheated oven until chicken is no longer pink in the center, about 25 minutes. Cool until easily handled, 5 to 10 minutes. Pull chicken apart. Slice sausage links.

Heat 2 tablespoons olive oil in a large skillet over medium heat. Add broccoli; cook and stir for 3 minutes. Stir in tomatoes, cherry peppers, jalapeno pepper, and garlic; cook until tomatoes soften, about 3 minutes. Stir in chicken and sausage slices.

Cut yellow squash into noodles using a spiralizer. Add to the skillet. Drizzle remaining 1 tablespoon olive oil over squash; toss with tongs until heated through, about 1 minute. Season with salt, pepper, and Italian seasoning. Melt butter on top.