Put your sliced onions in an ovenproof pan (a cast iron pan is best but any ovenproof pan will do). Drizzle on olive oil and sprinkle on tarragon. Bake in a 350-degree oven for at least an hour. Stir every 30 minutes until lightly browned on the edges of a few of the onion strings. You don't need to brown them all, and they don't need to completely shrivel. You just want them to get gummy and completely cooked.
The nice thing about this part of the recipe is you can be doing other things while you're caramelizing the onions. Set the table, arrange the flowers or do some of the other cooking.
Unroll your piecrust into a 10-inch spring form pan or other tart pan with a removable bottom. If the piecrust has been out of the refrigerator for 15 to 20 minutes it will unroll more easily. Just fit it into the pan and, if you need to, you can turn over the edges to form a crust along the sides that is one-half to one inch high. You don't have to be too picky.
Lay your prosciutto slices across the bottom to cover the entire bottom of the piecrust. They will overlap each other. Put in your onions and spread them across the prosciutto. Mix the eggs and cream with a fork until well mixed. You don't have to beat the mixture; just make sure the eggs are well broken up and the mixture is well blended. Spread the Gruyère and half of the Parmesan on top of the onions. Then pour the egg/cream mixture over the top.
Gently transfer the tart to your oven and bake for 30 minutes more at 350 degrees until the top is lightly browned and the filling is set. When you take the tart out of the oven, sprinkle on the rest of the Parmesan and it's ready to serve. Cut into pie-shaped wedges, large or small.