Step 1 In a medium saucepan over medium heat, melt the milk and butter. Add the flour and salt, stirring constantly, until the dough comes away from the sides of the pan, about 1 minute. Remove from heat and place the dough in a medium bowl.
Step 2 Beat the dough with a spoon or spatula until it cools down to lukewarm, 2 to 3 minutes. Add the eggs one at a time and mix until when you dip your fingers in the batter, a 1-inch string develops between your fingers as you separate them. Beat in the blue cheese until incorporated and refrigerate 1 hour.
Step 3Using a pastry bag fitted with a straight tip, pipe dough onto parchment in rows of 8. The circles should be about 1 1/2 inches round and half-inch high. Cut the parchment in strips of 8 beignets each.
Step 4Pour enough vegetable oil into a large saucepan to come a few inches up the sides. Heat the oil to 350 degrees. Using metal tongs, carefully dip each strip of beignets into the oil, pulling the strip of parchment out of the pan as the beignets release. Cook until deep golden brown and cooked in the center, about 2 minutes (1 minute per side). Carefully remove and place on paper towels to absorb excess oil. (Makes about 40 beignets.)