Heat your oven to 400°F.
Pour 2 tablespoons of the olive oil in the bottom of a 13-by-9-inch baking dish.
Arrange the tomatoes in the dish, cut side up.
Nestle garlic cloves around the dish.
Drizzle with another 2 tablespoons of the olive oil, and sprinkle with 1 teaspoon kosher salt and many grinds of black pepper.
Roast the tomatoes for 20 minutes, until everything is bubbly and juicy.
Remove from the oven to a trivet or cooling rack and use a fork to lightly mash the tomatoes and garlic.
Add drained beans and more salt and pepper if needed and stir to combine.
Return to the oven for 5 minutes.
Drizzle with remaining 1 tablespoon olive oil, scatter with basil, and eat right away, either as is or ladled over crostini.