Step 1Heat the oven to 300 degrees. Slice the tomatoes in half lengthwise and arrange them cut-side up in an 11 1/2-by-14-inch baking pan, preferably earthenware. They should fit tightly.
Step 2Separate the garlic into cloves and peel the cloves. Scatter them among the tomatoes. Season the tomatoes liberally with salt and pepper and pour over enough olive oil to come at least halfway up the sides of the pan. Bake, uncovered, until the tomatoes turn golden brown on top, at least 2 hours. Cool for at least 10 minutes.
Step 3Cut the baguette on a bias into half-inch slices. Toast the bread until lightly browned on both sides.
Step 4To serve, use a fork to remove each tomato slice from the pan (allowing excess oil to drip back into pan) and place it on a slice of toasted bread. Top each with a dab of fresh goat cheese, about 2 teaspoons.