Discard seeds and stems from peppers and slice from top to bottom into ¼” slices. Slice onion in thin slivers from top to bottom.
Preheat grill to 450˚F. Place a 12 inch cast iron skillet on the grill, close grill lid, and preheat for 5 minutes.
Add olive oil and butter to the skillet. Once butter is melted, add peppers and onions, then sprinkle with beef rub. Cook for 8-10 minutes, stirring often.
Once peppers and onions begin to brown, deglaze skillet with broth. Mix in salt, pepper, and sausages. Be sure sausages are in the broth (no need to be fully covered). Close grill lid and cook for 10 minutes.
After 10 minutes, remove skillet from the grill. Add sausage to the grill* and cook for 2-3 minutes per side, until browned and sausages reach 160˚F.
Meanwhile place buns, cut side down, on grill. Toast for 1-2 minutes.
Serve peppers and onions on the bun and top with sausage.
Notes
*Alternatively, brown sausages in a separate skillet on medium high heat. Toast buns in the oven or toaster if desired and serve with peppers, onions, and sausage.