Make the crêpes. Whisk eggs and salt together in a large bowl. Whisk in all flour until thoroughly blended. Gradually whisk in 1 cup of milk, stirring until completely blended. Cover and let batter rest for at least 1 hour; without this rest, the cooked crêpes will apparently be tough.
Lightly oil a small nonstick skillet or crêpe pan, spreading oil with a crumpled paper towel; heat the skillet over medium-high heat. Ladle about 2 to 3 tablespoons of batter into the skillet with a small ladle or measuring cup, tilting and rotating pan to spread the batter evenly over the entire bottom of the pan. Do this motion as you pour, not afterwards---otherwise, you'll end up with a thick center.
Cook the crêpe until the underside is lightly browned, about a minute or even less. You'll see the top side of the crêpe dry out and bubble as it nears doneness; the edges may start to curl or show signs of browning. Carefully loosening an edge of the crêpe with the tip of a spatula, work it under the crêpe and flip it. Cook until the second side is lightly browned, about 20 or 30 seconds or so. Slide the crêpe onto a plate.
If batter doesn't spread easily to create thin crêpes, whisk in more milk, 2 tablespoons at a time.
If serving immediately, fill and roll or fold the crêpe. Continue to cook crêpes with the remaining batter, oiling the pan as needed and stacking the crêpes as you go. You never want oil standing in the pan, just a nice shine over the entire surface. Cover plate of crêpes with aluminum foil and transfer to warmed oven while you prepare the filling [I had done all the prep work for the filling before starting the crêpes, so they didn't have to spend too much time in the oven].
Make the poulet aux champignons filling. Heat a large skillet over medium-high flame. Melt 1/2 tablespoon of butter with the olive oil, swirling pan to combine. Sauté mushrooms until they give off liquid and it evaporates, 4 to 5 minutes, stirring frequently. Stir in 1/2 teaspoon of herbes de Provence and cook until fragrant, about 45 seconds. Add 1/4 cup wine, and cook until it evaporates. Transfer mushrooms to bowl.
Add remaining 2 tablespoons of butter to pan. Sauté onions until softened, about 4 to 5 minutes. Stir in garlic and remaining herbes de Provence and cook until fragrant, about 45 seconds. Whisk flour into pan and stir constantly until flour is browned, about 3 minutes, making a quick roux. Gradually whisk in broth and wine, stirring constantly to combine flour and liquid to make a smooth sauce. I find this kind of whisk indispensable for the task.
Stir in chicken and mushrooms and warm through. Stir in cream and milk [or just milk]. If the sauce is too thick, gradually add more milk; but do so sparingly---you don't want the sauce too runny when you fill the crêpes.
Assemble crêpes. Lay crêpe on serving plate. Spoon filling down the center and fold sides over it. Repeat. Admire your handiwork, then devour it.