Preheat a grill pan over medium-high heat and preheat the broiler.
Drizzle the asparagus with some of the olive oil. Toss to coat and then sprinkle with salt and pepper. Place on the grill pan and cook until tender and grill marks form, 3 to 5 minutes per side, depending on the thickness of the asparagus. Remove, let cool slightly and cut into 2- to 3-inch pieces, about the size of the bread.
Brush the bread on both sides generously with oil and place on a baking sheet. Rub the garlic all over one side of each slice. Broil until golden and crispy, 2 minutes per side. Remove and let cool slightly.
Slather some of the goat cheese on the garlicky side of each piece of bread, then top each with 2 to 3 pieces of the grilled asparagus and a few of the cherry tomatoes. Return to the oven just until the cheese is melted and warmed, about 2 minutes.