For sauce, heat 1 tablespoon butter over medium heat in small saucepan. Add shallots and cook until translucent, 4-5 minutes.
Add garlic and thyme and cook until fragrant, about 1 minute.
Pour in red wine and bring to boil. Reduce to low and simmer for 5 minutes.
Add beef stock and bring to boil. Reduce to low and simmer for 15 minutes, or until sauce reaches desired consistency. Remove thyme sprigs.
Meanwhile, heat ½ tablespoon of butter in a large sauté pan over medium heat. Add beans and cook, stirring occasionally, until just tender, about 10 minutes. Remove beans from pan and set aside.
Heat remaining ½ tablespoon butter over low heat in same sauté pan and add remaining shallots. Cook over low, stirring regularly and adding more butter if needed, until shallots turn a nice caramel color, about 20 minutes. Caramelization takes time!
Set shallots aside and return beans to pan. Sauté over medium-low, just long enough to heat the beans and make them plump up, about 3 minutes. Place beans in a serving dish and top with wine sauce and shallots.