New Orleans-Style Chicory Beignets

In a large jar, shake the coffee with 2 cups of the milk. Refrigerate for 1 hour. Strain the milk through a fine sieve into a measuring cup and add as much fresh milk as needed to make 1 1/2 cups. Discard the coffee grounds. In the bowl of a standing electric mixer fitted with the dough hook, combine 1/4 cup of the coffee milk with the yeast and granulated sugar; let stand until foamy, 5 minutes. Add the remaining coffee milk, the 4 1/2 cups of bread flour and the butter and salt. Mix at low speed until the dough just comes together, 2 minutes. Increase the speed to medium and mix until the dough is smooth, 5 minutes. Transfer to a greased bowl, cover and let stand in a warm place until slightly risen, 2 hours. Divide the dough into 4 pieces. On a floured work surface, roll out one piece of dough a scant 1/3 inch thick. Cut into 2-inch squares, then cut each square into two triangles. Transfer to a floured baking sheet. Repeat with the remaining dough. Let stand for 20 minutes. In a saucepan, heat 2 inches of oil to 360 °. Working in batches, fry 10 or 12 beignets at a time until browned and cooked through, 5 minutes. Drain on paper towels and transfer to a bowl. Dust generously with confectioners’ sugar and serve immediately with vanilla ice cream and espresso.