I usually make these ahead of time and freeze them so they are ready to just pop in the oven before guests arrive. The sweetness of the dates is balanced out by the sharpness of the asiago and the salty bite of the prosciutto. —Braless Contessa
Heat the oven to 425 degrees and line a baking sheet with parchment paper. Place the butter, water, and salt in a medium saucepan and bring to a simmer. Reduce heat to medium and, working quickly, add the flour and stir vigorously until the flour is completely incorporated, a smooth dough forms and a slight film is starting to develop of the sides of the pan. Remove from heat and let cool for 2-3 minutes.
Add an egg and stir vigorously. At first the dough will appear to not take the egg but with a little patience you will find that the dough gives up and you will be able to incorporate the egg into the smooth dough. Repeat with the second egg.
Fold the cheese and the dates into the dough, reserving about two tablespoons of the cheese. Traditional gougeres are usually piped out into little balls, but I find it less messy to just scoop up the dough by the tablespoon and spoon them onto the baking sheet like a drop cookie. Sprinkle the remaining cheese and shreds of the prosciutto ontop and bake for about 25 minutes, reducing the temperature to 350 degrees after the first 10 minutes and rotating the baking sheet halfway. When the gougeres are finished, they will have a golden-brown exterior and will sound hallow when you tap them with your finger. Cool for 5 minutes and serve. Alternatively, you may bake these a little before they begin to brown and freeze them for 3 months. To reheat, just put them in a 350 degree oven and bake for about 10-15 minutes.