Step 1

In a Dutch oven, melt the butter over medium heat. Add the carrots and shallots, season to taste with salt and pepper, and cook, stirring occasionally, for 5 minutes.

Step 2

Add the mushrooms and cook, stirring occasionally, until all the vegetables are tender, 5 to 7 minutes.

Step 3

Add the thyme sprigs and garlic, and cook until fragrant, about 30 seconds. Add the wine and tomato paste and cook, stirring occasionally, until the wine is almost completely evaporated, 2 to 3 minutes.

Step 4

Add the beans, broth, Cognac, 1 teaspoon salt and 1/2 teaspoon pepper, and bring to a boil over medium-high heat. Turn the heat to low, partly cover, and simmer, stirring occasionally, until the sauce has reduced and thickened, 25 to 30 minutes.

Step 5

Remove and discard the thyme sprigs. Off the heat, stir in the parsley and balsamic vinegar; season to taste with salt and pepper. Divide among shallow bowls and sprinkle with more parsley, if desired.