Preheat grill to medium-high heat.
Brush both sides of mushroom caps with oil and season generously with salt and pepper.
Place mushrooms gill-side down on grill and cook until nicely charred, about 5 minutes. Flip and grill another 4–5 minutes until tender and juicy. During last 2 minutes, grill lemon halves cut-side down until caramelized.
Transfer mushrooms to serving platter, gill-side up, and evenly spoon pesto over each. Garnish with basil and drizzle with balsamic glaze, if desired. Serve with grilled lemon halves. Refrigerate any leftovers.
