Pat the beef chuck cubes dry with paper towels, then season them evenly with the salt and black pepper.
Heat 1 tablespoon of olive oil in a large heavy pot or Dutch oven over medium-high heat. Add half of the beef in a single layer and brown on all sides, about 5–7 minutes. Transfer the browned beef to a plate and repeat with the remaining 1 tablespoon of olive oil and the rest of the beef.
In the same pot, add the chopped bacon and cook over medium heat until the fat renders and the bacon becomes lightly crisp, about 5 minutes. Use a slotted spoon to transfer the bacon to the plate with the beef, leaving the fat in the pot.
Add the diced yellow onion to the pot and cook, stirring often, until softened and lightly golden, about 5–7 minutes. Stir in the minced garlic and cook for 1 minute until fragrant, being careful not to let it burn.
Sprinkle the all-purpose flour over the onion and garlic mixture. Stir well and cook for 1–2 minutes to remove the raw flour taste, forming a light paste on the bottom of the pot.
Slowly pour in the dry red wine while stirring and scraping the bottom of the pot with a wooden spoon to release any browned bits. Add the beef broth, tomato paste, dried thyme, and bay leaf, stirring until the tomato paste is fully dissolved.
Return the browned beef and bacon, along with any accumulated juices, to the pot. Stir to coat everything in the sauce, then bring the mixture to a gentle simmer over medium heat.
Reduce the heat to low, cover the pot with a lid, and let the beef bourguignon simmer gently for 60 minutes, stirring once or twice to prevent sticking.
After 60 minutes of simmering, add the sliced carrots to the pot, stirring them into the sauce. Cover again and continue to simmer on low heat for another 30 minutes.
While the beef and carrots continue to cook, melt the unsalted butter in a separate skillet over medium heat. Add the halved button mushrooms and cook for 6–8 minutes, stirring occasionally, until they are browned and have released most of their moisture.
Stir the browned mushrooms into the pot with the beef bourguignon. Cover and simmer on low heat for an additional 20–30 minutes, or until the beef is very tender and the sauce has thickened to a rich consistency.
About 25 minutes before you plan to serve, rinse the long-grain white rice under cold water until the water runs mostly clear. Place the rice, water, and salt for rice into a medium saucepan.
Bring the rice and water mixture to a boil over medium-high heat. Once boiling, reduce the heat to low, cover with a tight-fitting lid, and cook for 15 minutes without lifting the lid. After 15 minutes, remove the saucepan from the heat and let the rice stand, covered, for another 5–10 minutes, then gently fluff with a fork.
Remove the bay leaf from the beef bourguignon. Taste the sauce and adjust seasoning with a little more salt or black pepper if needed. Stir in the chopped fresh parsley just before serving.
To serve, spoon a bed of fluffy white rice onto each plate and ladle the hot beef bourguignon over the top, making sure each serving gets a good mix of beef, carrots, mushrooms, and sauce.