Place a rack in middle of oven; preheat to 450°.

Cut 1 large onion in half through root. Peel and discard skins. Finely chop and transfer to a medium bowl.

Wash, peel, and trim 3 medium carrots. Cut in half (or in quarters lengthwise if they’re large), then cut crosswise into ½" pieces. Add to bowl with onion.

Chop 2 celery stalks crosswise into ½" pieces. Add to bowl with the rest of the mirepoix.

Smash and peel 8 garlic cloves with the back of your knife. Add to bowl.

Strip stems from 2 bunches Tuscan kale and discard. Tear leaves into 2" pieces; set aside.

Cut rind off of 1 small Parmesan wedge; set aside.

Place 28 oz. canned tomatoes and their juices in a strainer set inside a medium bowl. Squeeze tomatoes and crush them with your hands while leaving them submerged in their liquid.

Tear ½ loaf crusty country bread into 1½" pieces.

Heat ⅓ cup extra-virgin oil in a medium Dutch oven or heavy pot over medium. Add bowl of mirepoix and 2 tsp. salt and cook, stirring occasionally, until vegetables are softened but not browned, 8–10 minutes.

Lift strainer full of tomatoes and give it a few shakes to remove any liquid. Add tomatoes (but not juices!) and cook, stirring occasionally, until some of the rawness is cooked off, about 10 minutes.

While tomatoes are cooking, drain and rinse 14 oz. canned cannellini beans, then add to pot along with Parmesan rind, tomato juices, ¾ tsp. red pepper flakes, and 4 cups water. Bring to a simmer.

Add kale in two additions, stirring often and allowing to wilt in between.

Add about one-third of torn bread and cook, stirring occasionally, until coated and warmed through, about 5 minutes more. Taste and adjust seasoning.

Remove from heat. Place remaining torn bread chunks on top of stew. Drizzle generously with olive oil.

Transfer pot to oven and bake stew until thick, bubbling, and bread is golden brown on top, 10–15 minutes.

Ladle stew into bowls, drizzle each generously with olive oil, and grate lots of Parmesan over.