Prepare the ingredients: Cut the beef chuck into 1-inch cubes. Quarter the cremini mushrooms. Peel the pearl onions or chop the yellow onion into large chunks. Slice the carrots into thick rounds. Mince the garlic. Peel and cube the potatoes.

In a large skillet, heat olive oil over medium-high heat. Sear beef cubes until browned on all sides. Remove and set aside.

In the same skillet, add onions and garlic. Sauté until fragrant, about 2 minutes. Add mushrooms and cook until they release their moisture and begin to brown.

Add red wine to deglaze the pan, scraping the bottom to release any browned bits. Allow the wine to reduce by half.

Return the beef to the skillet. Add beef stock, thyme, bay leaf, salt, and pepper. Bring to a simmer. Reduce heat to low, cover, and let cook for 1 hour, stirring occasionally.

While the beef is cooking, boil the potatoes in a pot of salted water until tender, about 15-20 minutes.

In another pan, melt 1 tbsp of butter and add sliced carrots. Sauté for 3 minutes, then add 1/4 cup of water. Cover and cook until tender, about 10 minutes. Season with salt and pepper.

Drain the boiled potatoes. Mash with 1 tbsp butter and milk until smooth. Season with salt and pepper to taste.

Check the bourguignon for seasoning, adjust salt and pepper as needed. Discard the bay leaf before serving.

To serve, plate the mashed potatoes, top with beef bourguignon, and place the braised carrots on the side.