Adjust oven rack to lower-middle position and heat oven to 325 degrees.
Season beef with salt and pepper. Heat oil in Dutch oven over medium-high heat until shimmering. Add onions and ¼ teaspoon salt and cook, stirring occasionally, until well browned, 8 to 10 minutes.
Add tomato paste and garlic and cook until rust-colored and fragrant, about 2 minutes. Stir in flour and cook for 1 minute. Whisk in 2 cups broth, sugar, and 1 tsp thyme, scraping up any browned bits. Bring to simmer and cook until slightly thickened, about 3 minutes. Stir in beef and return to simmer.
Transfer to oven and cook, uncovered, for 90 minutes, stirring halfway through cooking.
Stir in potatoes and carrots, keeping beef on top when possible. Add broth as necessary to cover the vegetables. Cook for 45 minutes and add green beans, making sure to submerge them in the broth. Continue cooking until beef and vegetables are tender, about 45 minutes longer. Add 1-2 tsp thyme, season with salt/pepper to taste, and serve.