In a medium saucepan, heat the milk, water, vodka, sugar, salt, and butter and bring to a boil. Stir until all the butter has melted.
Add in the flour and stir with a wooden spoon until a soft dough ball forms. Keep mixing the dough around the pan for 2-3 minutes to cook the flour.
Move the dough to the bowl of a stand mixer fitted with the paddle attachment. Turn the mixer up to medium and add the eggs one at a time. Allow each egg to be fully mixed before adding the next one. After you add the first two eggs, lightly beat the remaining one and add it in 1/4 at a time. Keep mixing until your dough is glossy but thick enough to hold a V shape at the end of the paddle. (I wound up using 2 1/2 eggs in total.)
Preheat oven to 425° F and line two baking sheets with parchment paper.
Transfer your choux pastry to a pastry bag and cut off the end. Pipe the dough into 3-4 inch logs about 1 1/2 inches apart. You should be able to pipe 9-10 logs. If you have large tips of dough at the end of your éclairs, dab your finger in a little water and smooth them down.
Place your baking trays in the oven and turn the temperature down to 375° F. Bake for 25-30 minutes or until the éclairs rise and are golden brown.
Turn off the oven and let the éclairs cool for 15 minutes with the door open. Remove the trays from the oven and let the éclairs finish cooling.