Preheat oven to 325 degrees or set a slow cooker on low.
Cut meat into large chunks, about 1-inch pieces and pat dry.
Season meat with 2 teaspoons salt and 1 teaspoon black pepper.
Heat the oil in a large heavy-bottom soup pot or Dutch oven over medium-high heat.
Add meat in small batches to brown, making sure to turn the meat periodically so that it can brown on all sides. Remove each batch of browned meat to a large bowl and set aside.
When all meat is browned and removed to the bowl, add the onion and celery and continue browning the vegetables lightly, without scorching, about 5 minutes; remove vegetables to the bowl with the meat and set aside.
Add garlic to the pot and saute lightly for about 1 minute, and then immediately stir in 1 cup of water.
Turn heat to high and bring to a boil, stirring and scraping the bottom to remove browned bits from the bottom of the pan; reduce liquid by half, stirring often.
Stir in tomato paste and continue cooking for another minute or two.
Add remaining water and bouillon.
Reduce heat to medium-low.
Add everything back to the pot, including the pearl onions, potatoes, mushrooms and carrots, stir to combine.
In a small glass or bowl, whisk together ¼ cup all-purpose flour and ½ cup cold water; stir into vegetable-meat mixture and stir to combine, remove from heat.
If using the oven method, place a lid onto the Dutch oven or pot and place in the middle rack in the preheated oven and braise for 2 to 2 ½ hours.
If using the slow cooker method, transfer stew mixture to the bowl of a slow cooker and cook on low for approximately 6 hours with the lid on.
When stew is finished, stir in fresh minced thyme and adjust seasoning to taste by adding salt and pepper.
This stew gets even better if made a day ahead and refrigerated overnight and then reheated the next day!