Preheat the oven to 400°F. Trim and quarter the Brussels sprouts. Slice the cremini mushrooms. Peel and dice the onion. Peel and dice the carrot. Peel and mince the garlic.
Roast the sprouts
Add Brussels sprouts to a baking sheet and toss with 1 tbsp olive oil and a pinch of salt and pepper. Roast until tender and browned in places, about 10 to 12 minutes.
Sear the mushrooms
Place a small saucepan over high heat with 2 cups water. Cover and bring to a boil for the polenta. Place a medium saucepan over high heat with 1 tbsp olive oil. Once hot, add the sliced mushrooms and cook until browned in places, about 4 to 5 minutes. Transfer the mushrooms to a plate.
Start the bourguignon
Return the medium saucepan to medium-high heat with 1 tbsp olive oil. Add the diced onion, diced carrot, dried thyme, ½ tsp salt, and ¼ tsp pepper. Cook until softened, about 3 to 5 minutes. Add the minced garlic and tomato paste and cook until aromatic, about 1 minute. Add the flour, stir, and reduce heat to medium. Cook, stirring frequently, until the flour smells toasted, about 1 to 2 minutes.
Finish the bourguignon
Add 1 cup water and the concentrated vegetable broth to the saucepan with the vegetables. Stir with a wooden spoon and cook until sauce comes to a boil and thickens, about 4 to 5 minutes. Add the seared mushrooms, taste the mushroom bourguignon and adjust seasoning with salt and pepper.
Cook the polenta & serve
Once the water in the small saucepan is boiling, slowly add the polenta while whisking continuously until it thickens, about 2 to 3 minutes. Remove from the heat, add the butter, and whisk well. Divide the polenta between plates and top with the mushroom bourguignon. Serve with roasted Brussels sprouts. Dig in!