Place pepper strips and onion in bottom of slow-cooker. Arrange chicken sausage on top and then pour diced tomatoes and tomato sauce on top. Cover and cook on low for 8 hours or on high for 4 hours.
Transfer warm sausage to a board and slice into 1/4-inch strips. Return sausage to pot and stir to mix; keep warm.
Brush a grill pan with oil and place over medium heat. Brush bread slices on both sides with olive oil, then toast in batches, turning, until crisp and golden. Rub each slice lightly with garlic.
Place 1 slice of toast on each plate. Spoon sausage mixture on top and sprinkle with basil and cheese. Top with second slice of toast.