Combine basil, cheese, oil and garlic in a food processor or blender and process until well blended. Add yogurt and process until smooth. Season with salt and pepper and set aside.
Preheat the broiler. Place bagels or muffins cut-side up on a baking sheet. Broil until lightly toasted, 1 to 2 minutes. Spread each half with the reserved basil mixture and top with a few slices of tomato. Season with salt and pepper and broil until hot, 1 to 2 minutes.