In a large bowl, combine warm water (about 115 degrees), yeast and sugar. Allow to bloom and become foamy, about 10 to 12 minutes.
Whisk in evaporated milk, espresso and egg. Whisk in half of the flour and salt. Switch to a spoon and mix in the shortening and then the rest of the flour just until crumbly.
Dump out the mixture onto a board. Knead with your hands just until combined, about 2 minutes. Be careful not to over-knead. Place dough in a lightly oiled bowl, flip it over once to coat the other side in oil, cover and allow to rise until doubled in size.
Just before frying, make the glaze by whisking all ingredients together until smooth. Set aside.
In a cast-iron skillet or deep fryer, heat a neutral cooking oil to 380 degrees. Meanwhile, transfer the dough onto a well-floured surface and gently roll out until 1/4 inch thick. Square off the edges with a knife or pastry cutter and cut the dough into 14 to 16 squares.
Fry a few squares at a time. Carefully flip them over every 10 seconds, until golden brown and puffed on both sides. Drain on a rack or paper towel.
While the beignets are still warm, lightly dust with powdered sugar and drizzle the glaze on top.