Heat olive oil in a large skillet over medium-high heat until shimmering. Season chicken pieces with salt and pepper on both sides, then place them in the hot skillet. Cook for 4-5 minutes per side until golden brown, turning only once for better crust development.
Remove chicken to a clean plate once browned but not fully cooked through. Add diced onion to the same skillet and sauté for 2-3 minutes until softened and fragrant, scraping up browned bits from the bottom.
Stir in minced garlic and cook for exactly 30 seconds until fragrant. Add Italian seasoning and paprika, stirring constantly for another 30 seconds to bloom the spices and intensify their flavors.
Pour chicken broth and canned diced tomatoes (with juice) into the skillet, stirring to combine. Return the browned chicken pieces to the skillet chicken recipe, nestling them into the sauce. Simmer for 8-10 minutes until the chicken reaches 165°F internally.
Add sliced bell peppers and mushrooms directly to the simmering sauce, stirring gently. Continue cooking for 3-4 minutes until vegetables soften slightly while retaining some crunch and texture.
Reduce heat to low and stir in heavy cream, distributing it evenly throughout the sauce. Add fresh parsley and taste for seasoning, adjusting salt and pepper as needed for your preference.
Let the dish rest off heat for 2 minutes before serving, allowing flavors to meld and sauce to thicken slightly for better plate presentation.