In a stand mixer bowl, stir together ½ cup water, sugar, and yeast. Allow the yeast to bloom for 5 minutes.
Add the evaporated milk, eggs, and salt to the yeast mixture and beat just until combined.
In a large measuring cup, stir vegetable shortening into the remaining warm water. Mix into yeast mixture. If the water is not warm enough to melt the shortening, heat it in the microwave for 30 to 60 seconds.
Add the cocoa powder and 4 cups of bread flour to the mixing bowl and blend until smooth. Slowly add remaining bread flour.
Transfer dough to an oiled bowl, turning the dough to oil all sides. Cover with plastic wrap.
The dough can be refrigerated for up to 24 hours or allowed to rise in a warm, draft-free location until it doubles in size.
Heat vegetable oil in a fryer or dutch oven until 360 degrees.
Turn dough out onto a lightly floured surface and gently shape into a rectangle. Roll the dough to ¼ inch thickness.
With a sharp knife or pizza cutter, cut the dough into about 40 rectangular pieces.
Fry the beignets in small batches about 2 to 3 minutes on each side or until golden. Remove and drain on paper toweling.
Sift together the cocoa powder and powdered sugar for the powdered sugar topping.
Before serving, toss with the chocolate powdered sugar.
Notes
You can pre-make this dough and store it in the fridge for up to 24 hours.