Rinse 300 g dried cannellini beans and pick out any stones. Cover with 1.5 L cold water in a bowl and soak for 8 to 12 hours at room temperature. Drain and discard the soaking water.
Heat the oven to 150 C / 300 F with a rack in the lower third. Lightly crush the garlic cloves with the flat of a knife and crush the tomatoes by hand.
Put the drained beans in a 3-quart / 2.8 L Dutch oven (22 cm / 9-inch) with 700 ml cold water, 4 tbsp oil, garlic, sage, tomatoes, salt, and pepper. Bring to a bare simmer over medium heat, about 10 minutes, and skim off any foam.
Press a sheet of parchment over the surface, cover with the lid, and bake for 90 minutes without stirring. The beans are done when one mashes easily between your fingers, tastes creamy at the center, and the liquid is loose and glossy. If the centers are chalky, the beans are old, so bake 15 to 20 minutes more.
Take the pot out and leave it covered for 10 minutes. Taste and adjust the salt, stir in the remaining 1 tbsp raw olive oil, and serve warm with some of the cooking liquid.