Slice the chicken sausage links into ½-inch thick coins. Heat olive oil in a large skillet over medium-high heat until shimmering, then add sausage pieces and cook for 3-4 minutes until lightly browned on both sides, stirring occasionally.
Remove cooked sausage to a plate temporarily. Add diced onion to the same skillet and sauté for 2 minutes until it begins softening and releasing its sweet aroma throughout your kitchen.
Stir in minced garlic, then add sliced red and yellow bell peppers along with mushroom slices. Cook this vegetable mixture for 3-4 minutes, stirring frequently until peppers begin to soften and vegetables release their natural juices.
Add tomato paste and stir constantly for 1 minute to cook out the raw flavor and develop deeper, more complex taste notes that build your sauce foundation.
Pour in chicken broth, diced tomatoes with their juice, Italian seasoning, paprika, and red pepper flakes. Return the saucy crowd sausage skillet ingredients to the pan with the baby potatoes and bring everything to a simmer.
Reduce heat to medium and simmer for 12-15 minutes until potatoes are fork-tender and the sauce has thickened slightly, coating the back of a spoon beautifully.
Taste and adjust seasonings with salt and pepper as needed. Stir in fresh parsley just before serving for bright, herbaceous finish that brightens the entire dish.