Preheat the oven to 325 F.
Trim and cube the beef into 2 inch pieces. [We used pre-cut stewing beef.]
Slice or scissor the bacon strips into 1- or 2-inch pieces.
Skin and slice the onions and shallots. [Or used pre-diced onions for a cheat.]
Place clean, reusable cloth towels or disposable paper towels on a large baking sheet.
Place a mesh strainer over a clean bowl.
In a large dutch oven or oven-ready casserole, heat the oil over medium-high heat.
In batches, add the beef and brown on all sides.
Remove the beef to the lined pan.
In the hot dutch oven, add the bacon and cook for about 3-5 minutes, until the bacon has begun to crisp. [I like soft bacon, so I tend to undercook slightly.]
Remove the bacon to the lined pan. [It's okay to spread these in and around the beef chunks. They will go in the same dish, soon enough.]
In the same hot dutch oven, add the onions and shallots and cook for about 3-5 minutes, until they begin to soften.
Remove the onions and shallots to the strainer over the bowl. [These will NOT go back into the casserole just yet!]
To the hot and once-again-empty dutch oven, add about 1 cup of the stock and 1/4 cup of the wine.
With a flat whisk or wooden spoon, stir the the liquid about in the browned bits in the bottom of the vessel for about 60 seconds or until it begins to boil.
Place the flour in a small bowl.
Add 1/4 cup of the boiling liquid to the small bowl and, with a fork or small whisk, whisk the flour vigorously until it combines completely with the hot liquid.
Add another 1/4 cup of the boiling liquid to the flour/stock mixture and whisk vigorously to incorporate.
Add the flour/stock mixture back to the vessel of boiling liquid.
Add the remaining stock and wine to the pan and whisk vigorously to incorporate.
Allow the mixture to boil for a minute or two until it thickens slightly.
Add the beef and bacon back into this pot. [Leave the onions aside for the first 60-90 minutes of cooking!]
Skin and crush the cloves of garlic with the back of a spoon.
Add the crushed garlic, the bay leaves, and the bouquet garni to the dutch oven.
Season conservatively with salt and pepper.
Stir gently, cover, and place the dutch oven into the hot oven.
Cook for 60-90 minutes [the longer, the better - but, not everyone has the time!]
Remove the dutch oven from the hot oven for a moment.
Add the shallots, onions, and mushrooms, stir, and cover.
Return to the oven and cook for about 60 minutes [or more, if your cut of beef isn't as tender as you'd like].
Remove the vessel from the oven and remove the cover.
Remove the bouquet garni and the bay leaves and compost them.
Taste the liquid and add additional salt and pepper if required. [We tend to leave the extra seasoning up to our guests.]
Spoon the boeuf bourg. into bowls.
Enjoy with a large loaf of french bread or some fantastic roasted potatoes [or both!]