Melt the butter into the milk in a small saucepan set over low heat, ensuring the mixture does not come to a boil.
Transfer this warm mixture into your stand mixer bowl, then whisk in the sugar until completely dissolved.
Let it sit and cool down until the mixing bowl feels warm to the touch and no visible steam remains.
Evenly sprinkle the active dry yeast across the surface, letting it stand for 5 to 10 minutes until it becomes frothy.
Incorporate the eggs, vanilla extract, kosher salt, and all-purpose flour into the bowl.
Attach the dough hook and blend on low speed until combined. Raise the speed slightly to medium-low and knead for 8 to 10 minutes until you have a smooth, elastic, and slightly tacky dough.
Move the dough to a lightly greased bowl, cover it up, and let it rise for about 1 1/2 to 2 hours, or until its size has doubled.
Deflate the dough by punching it down, then chill it in the refrigerator for at least 30 minutes.
Roll the chilled dough out to a 1/4-inch thickness, then cut it into 2 1/2-inch squares.
Loosely drape a cover over the squares and let them rest for 20 to 30 minutes.
Bring your neutral frying oil up to a temperature of 360°F.
Cook the beignets in the hot oil for 1 to 2 minutes on each side until puffed and beautifully golden brown.
Use a slotted utensil to transfer them to a wire cooling rack for 1 minute.
Prepare the glaze by thoroughly whisking the powdered sugar, milk, vanilla, and salt together until completely
