In a medium pot with a lid on medium-low heat, add the olive oil, and when shimmering, add the garlic. Cook for 1 minute, until the garlic colors. Then add the flour, swirling around in the garlic-oil until well-mixed.
Add the chopped shallots and wine, along with some salt and pepper, stir and cook, covered, for 15-20 minutes until the shallots are very soft and caramelized.
While it's cooking, crisp the baguette slices. Arrange them on a sheet pan and brush one side with olive oil. Place the bread slices under the broiler. Turn once, brushing the other side with the oil, so the bread gets nicely crisped up but not burnt, about a minute per side. Remove the bread and set aside.
When onion mixture is done, add a cup of water and stir, deglazing the bottom of the pot. Let reduce slightly, about two minutes.
If you‘d like a smoother sauce, you can pass the mixture through a food mill at this point. I didnt bother. Instead, I used a hand blender to puree everything.
Either way, once pureed, add the mushroom caps and cook, covered, about 5 minutes, until the mushrooms are done but still a little firm.
To serve, spread a little of the onion puree on the baguette slice, top with a mushroom and some more of the puree. Then another mushroom and more puree. Skewer the mushrooms in place and top with parsley.