Place a large cast iron skillet over medium-high heat. Once hot, char the bell peppers in a dry skillet, until lightly blistered. Remove the peppers and set aside.
Add the butter, onions, and garlic to the skillet. Sauté for 2-3 minutes, then push onions to the side of the pan.
Add the chicken, mushrooms, thyme, smoked paprika, 1 ½ teaspoons salt, and ½ teaspoon ground black pepper. Sauté, stirring occasionally, until the chicken is cooked through, about 6-8 minutes.
Toss the blistered peppers back into the skillet. Cook another 2 minutes. Taste, then salt and pepper as needed.
Serve as-is, or on soft bubbly bread rolls, just like in Croatia. (I find soft ciabatta buns are the closest thing to Croatian sandwich bread found in the US.)
