Heat grill to low. Brush baguette slices on both sides with olive oil. Grill on one side until golden, 1 to 2 minutes. Rub grilled sides with halved garlic clove and top with crumbled cotija or feta cheese. Return to grill, cover, and cook until undersides of baguette are golden and cheese has softened, 1 to 2 minutes. Drizzle with more oil.