1.In a shallow dish, whisk together oil, vinegar, garlic, 1 teaspoon salt, and 1/4 teaspoon pepper. Add bell pepper and mushrooms; toss gently to coat. Marinate at room temperature for 30 minutes (or refrigerate, up to overnight).
2. Heat grill to medium; lightly oil grates. Grill bell pepper, skin side down, until blackened, about 10 minutes; remove from grill. When cool enough to handle, remove and discard skin; set bell pepper aside. Grill mushrooms, covered, until lightly charred and tender, 3 to 4 minutes per side.
3.Dividing evenly, top bottom half of each bun with bell pepper, mushrooms, goat cheese, and lettuce. Close burgers, and serve immediately.