Half of the beans are mashed while the rest are left whole, giving this hearty one-pot stew a wonderfully chunky texture. Toasted ciabatta flavored with sage and garlic makes the perfect accompaniment.
Heat 3 tablespoons oil in a large straight-sided skillet over medium-high. Add bread; cook, flipping once and adding sage sprigs halfway through, until toasted, 10 minutes. Transfer to a plate; lightly rub one side with whole garlic clove. Season with salt.
Discard oil; return skillet to medium-high heat. Add remaining 1 tablespoon oil, sliced garlic, carrots, and chopped sage; season with salt and pepper flakes. Cook, stirring, until garlic is golden. Add wine; cook until evaporated, 2 minutes. Stir in beans and broth. Bring to a boil, then reduce heat and simmer until carrots are tender and liquid has reduced slightly, 25 minutes. Transfer 1 cup beans to a bowl; mash and return to pot. Stir in greens just until wilted; season with salt. Serve over toast, with cheese and a drizzle of oil.