1. Season roast generously with salt and pepper. Heat a large Dutch oven or other heavy pot over medium-high heat. Add 3 tablespoons oil; swirl to coat. Sear meat, turning occasionally, until deep brown all over, about 12 minutes. Transfer roast to a plate.

2. Reduce heat to medium and add onions, garlic, remaining 1 tablespoon oil, and a splash of water. Raise heat to medium-high and cook, stirring frequently, until onions are translucent, about 8 minutes. Stir in sugar, vinegar, wine, thyme, peppercorns, juniper, bay leaves, and cloves. Bring to a boil, then remove from heat and stir in applesauce. Add roast; turn to coat. Let cool 20 minutes, then cover and refrigerate at least 8 hours and up to 24 hours, turning once.

3. Preheat oven to 300 degrees. Transfer Dutch oven from refrigerator to stove top; turn roast in liquid. Bring mixture to a boil over high heat. Cover; transfer to oven and bake 2 1/2 hours, turning roast every 30 minutes. Uncover and bake until roast is tender and the tip of a knife pierces through easily, about 30 minutes more. Remove roast; transfer to a cutting board to rest.

4. Meanwhile, cook sauce over high heat until reduced to a silky consistency, 8 to 10 minutes. Taste sauce; add 1 to 2 teaspoons sugar if too acidic.

5. Cut roast against the grain into thin slices; return to pot. Divide sliced meat with sauce, dumplings, and reserved croutons among plates. Top with thyme and serve.