Preheat oven to 375º and position a rack in middle of oven.
Cut baguette into 1/4-inch slices.
Spread on baking sheet and bake until edges are golden, 7 to 10 minutes.
Transfer to plate and set aside.
Chop one tomato half into small pieces.
Heat oil in medium saucepan over medium heat.
Add chopped garlic and sauté until toasted, about 3 minutes.
Add beans, 1/2 cup water, and salt and pepper.
Simmer until most of liquid has evaporated, about 5 minutes.
Add vinegar and mash with fork until roughly pureed.
The puree can be made one or two days ahead of time and refrigerated.
Bring to room temperature before using.
Rub each slice of bread lightly with the whole garlic clove, then with the remaining half tomato.
Spoon about 1 Tbsp of bean puree onto each slice and top with chopped tomato.
Drizzle with olive oil and serve.