Heat olive oil in a skillet. Saute onion, peppers, garlic and carrot for 1-2 minutes. Add hot sauce and cheddar cheese. Allow cheese to start to melt. Remove from heat.
Slice bread into 1 inch slices. Pour cheese mixture on one slice of bread , add chives, and top it with another slice to form a sandwich. May make open faced, in which case you would only grill one side.
Grill until grill marks are formed, about 30 seconds on each side. In the winter I grill in a grill pan.