Step 1Combine the cheese, 2 tablespoons of basil, onion and 1 teaspoon of olive oil. Add salt and pepper to taste. (This can be made a day ahead and refrigerated. Serve at room temperature.)
Step 2Heat the grill or broiler.
Step 3Cut the sides off the pepper in 4 slabs. Place them skin side down on the grill or skin side up beneath the broiler until blackened, about 5 minutes. Wrap in foil. When just cool enough to handle, remove the skins. Cut into 1-inch strips and toss with the remaining teaspoon of olive oil and the vinegar. (This can be made a day ahead and refrigerated. Before using, bring to room temperature.) Toss with the remaining 2 tablespoons of basil.
Step 4Spread the goat cheese mixture on the warm bruschetta, dividing evenly. Top with the red peppers.