Combine yeast, sugar and 125ml (½ cup) lukewarm water in the bowl of an electric mixer and stir to dissolve yeast. Set aside for 10 minutes or until mixture bubbles. Add egg, evaporated milk and a pinch of salt, and stir to combine. Stir in half the flour until combined, then stir in the Copha until combined. Gradually stir in the remaining flour until dough is well combined. Using an electric mixer fitted with a dough hook, knead for 5 minutes or until smooth and elastic. (Alternatively, knead by hand on a lightly floured work surface.) Place dough in a large greased bowl, cover with plastic wrap and set aside in a warm, draught-free place for 2 hours or until dough doubles in size.
Lightly dust 2 trays with flour. Punch down dough, then turn out onto a lightly floured work surface and roll out into an 8mm-thick rectangle. Cut dough on the diagonal into 20 x 6cm x 7cm diamonds. Place on trays and cover with a tea towel. Set aside for 30 minutes or until dough doubles in size.
Fill a deep-fryer or large saucepan one-third full with oil and heat over medium heat to 180°C (or until a cube of bread turns golden in 15 seconds). Working in batches, pinch the edges and centre of each diamond, pulling to create air pockets. Gently drop into oil and deep-fry, turning halfway, for 4 minutes or until crisp, golden and cooked through. Remove with a slotted spoon and drain on paper towel.
Dust beignets generously with icing sugar and serve warm.