Heat the butter and olive oil in a large stockpot. Add the onions and sauté until onions begin to soften, about 8 minutes. Reduce the heat to low; cook until onions are caramelized, stirring occasionally, about 20 minutes. Add garlic, mustard and thyme. Stir in flour and cook, stirring frequently, until well coated, for 3 minutes.
Gradually stir in the Cognac, stock and white wine. Bring to a boil, reduce to low heat. Season to taste with salt and pepper. Simmer uncovered over medium heat for about 20 minutes. Cover and chill. Bring to a simmer before serving.
Preheat broiler. Place baguette slices on a large baking sheet. Spread goat cheese on slices, dividing equally. Broil goat cheese croutons until cheese begins to brown in spots, about 30 seconds. Divide soup among 8 bowls. Top with crotons.