Heat the oven to 425° Line baking sheets with parchment paper or with a silicone mat.
In a large skillet, over medium-high heat, melt 1 tablespoon of butter.
Add the mushrooms, shallots and a pinch of salt.
Cook until tender and lightly browned, 4 to 5 minutes. Set aside.
In a medium saucepan over medium heat, combine 1 stick of butter, water, milk, a pinch of salt and pepper.
Bring to a simmer, then add the flour all at once.
Stir vigorously with a wooden spoon, until the mixture becomes a ball that separates from the pan, 1 to 2 minutes.
Stir for an additional minute to dry out ball slightly.
Transfer contents to a large bowl.
With an electric mixer, beat on medium speed for 2 minutes to allow the mixture to cool slightly.
Add the eggs, one at a time, beating thoroughly after each addition.
Stir in the reserved mushroom mixture and the blue cheese.
Scooping by the tablespoonful, place walnut-sized dollops on the prepared baking sheets, leaving 1 1/2 inches of space between each or transfer the dough into a large zip-lock plastic baggie. Snip off one of the corners and pipe the mixture into place on the prepared baking sheets.
Bake for 10 minutes, turn heat down to 375° and bake an additional 20 to 25 minutes or until golden brown.