Adjust oven rack to lower-middle position and heat oven to 300°F.

If using bone in ribs, remove bone. Trim excess fat and pat beef dry with paper towels. Season with 2 tsp salt and 1 tsp pepper.

Heat 1 tbsp oil in large heavy-bottomed Dutch oven over medium-high heat. Add half of the ribs and cook, without moving, until well browned, 4 to 6 minutes. Turn ribs and continue to cook on second side until well browned, 4 to 6 minutes longer, reducing heat if fat begins to smoke. Transfer ribs to medium bowl. Repeat with remaining tbsp oil and ribs.

Reduce heat to medium, add onions, and cook, stirring occasionally, until softened and beginning to brown, 12 to 15 minutes. (If onions begin to darken too quickly, add 1 to 2 tablespoons water to pan.)

Add tomato paste and cook, stirring constantly, until it browns on sides and bottom of pan, about 2 minutes.

Add garlic and cook until aromatic, about 30 seconds. Increase heat to medium-high, add wine and simmer, scraping bottom of pan with wooden spoon to loosen browned bits, until reduced by half, 8 to 10 minutes.

Add broth, carrots, thyme, and bay leaf. Add ribs and any accumulated juices to pot then cover and bring to simmer. Transfer pot to oven and cook, using tongs to turn meat twice during cooking, until fork slips easily in and out of ribs, 2 to 2 ½ hours.

Place water in small bowl and sprinkle gelatin on top and let stand at least 5 minutes.

Using tongs, transfer ribs and carrots to serving platter and tent with foil. Strain cooking liquid through a fine-mesh strainer into fat separator or bowl, pressing on solids to extract as much liquid as possible; discard solids. Allow liquid to settle about 5 minutes and strain off fat. Return cooking liquid to Dutch oven and cook over medium heat until reduced to 1 cup, 5 to 10 minutes.

Remove from heat and stir in gelatin mixture. Season with salt and pepper. Pour sauce over ribs and serve over egg noodles.