Preheat a 4.5- or 6.5-qt. sauce pan over medium-high heat until rim of pan is hot to the touch. Add 2 Tbsp. of the oil and heat for about 1 more minute.
Mix in onions and garlic. Reduce heat to medium; cover and cook, stirring occasionally, until onions are very soft, about 10 minutes. Reduce heat to medium-low; uncover and cook, stirring often, until onions are golden, about 15 - 20 more minutes.
Add as many bratwurst and kielbasa as will fit in pan without crowding. Cook, turning as needed, until sausages are browned on all sides. As sausages brown, remove from pan and keep warm.
When all sausages are browned, stir flour into onion mixture. Gradually add broth; increase heat to medium and cook. Stir until sauce boils and thickens.
Blend in ketchup, mustard and horseradish. Cook, stirring often, until sauce is hot. Lightly mix sausages into sauce; spoon sausages and sauce into rolls (or place browned sausages in rolls direct from grill; spoon sauce over them).