Season the osso buco pieces with salt and black pepper. Heat olive oil in a large Dutch oven over medium-high heat. Add the osso buco and brown on all sides, about 10 minutes total. Remove from pot and set aside.

Sauté the Vegetables

In the same pot, add onions, carrots, and celery. Sauté until softened, about 5-7 minutes. Stir in minced garlic and cook for an additional minute.

Deglaze and Braise

Pour in the white wine, scraping up any browned bits. Add the broth, bay leaves, and thyme. Return the osso buco to the pot. Bring to a simmer, cover, and reduce heat to low. Cook for 1.5 to 2 hours until tender.

Prepare the Fingerling Potatoes

While the osso buco is cooking, boil the fingerling potatoes in salted water until tender, about 15-20 minutes. Drain and set aside.

Cook the Kale

In a separate pan, sauté the chopped kale in a little olive oil until wilted, about 5 minutes. Season with salt and pepper.

Make the Caraway Carrot Purée

In a small saucepan, combine the halved carrots, caraway seeds, and vegetable broth. Simmer until the carrots are tender, about 15 minutes. Blend until smooth, adding a splash of heavy cream for richness.

Plate the Dish

To serve, place fingerling potatoes on a plate, top with osso buco, and add sautéed kale. Drizzle with caraway carrot purée.