How to Make It
Put the beans in a medium saucepan and add enough water to cover by 2 inches. Add the 2 whole garlic cloves, thyme sprigs and bay leaf and bring to a simmer over moderate heat. Cover partially and simmer, stirring occasionally, until the beans are tender, about 1 1/2 hours.
Discard the thyme sprigs and bay leaf. Transfer the beans, garlic and cooking liquid to a food processor and puree. Press the puree through a coarse strainer into a bowl. Stir in the olive oil and lemon juice and season with table salt and pepper.
Spread the cucumber slices in a large glass baking dish. In a bowl, combine the minced garlic with the vinegar, sugar, kosher salt and crushed red pepper; stir to dissolve the sugar and salt. Pour the dressing over the cucumber and toss. Refrigerate for 1 to 2 hours, tossing occasionally.
Just before serving, spread each slice of toast with white bean puree and top with cucumber slices. Arrange the crostini on a platter and serve.