First, make the crust dough. Combine the flour, baking powder, seasoned salt, and dried tarragon in the bowl of a food processor. Pulse it a couple of times to aerate those dry ingredients. Then add in the butter and pulse it some more until it resembles pebbly sand. Finally, add in the ice water and pulse it until it comes together into a gorgeous dough. Take the dough and form it into ball. Place it on a big sheet of plastic wrap and press it into a small disc. Wrap the disc in the plastic wrap and chill it for 30 minutes in the refrigerator.
Once it has chilled, pre-heat the oven to 350 and spray a 9 inch tart pan that has a removable bottom well with cooking spray. Roll out the disc of dough until it can more than fit into the tart pan. Press it into the pan firmly and trim off the excess. Line the crust with foil and fill it with either dried beans or pie weights and blind bake the crust for 30-35 minutes. It should become golden around the edges. When it is done, take it out and let it cool. Remove the foil and pie weights.
While the crust bakes and cools, prepare the filling. Heat the olive oil in a large skillet over medium high heat. Add the potatoes and onions to let them soften and start to develop color for about 4-5 minutes. Then add the ham and peas just to warm them through for a couple of minutes. Take the pan off of the heat and set it aside. Whisk the eggs, milk, salt and crushed red pepper together in a bowl. Then it is time to assemble the quiche!
Spoon the ham and veggie mixture into the cooled crust and make sure it is evenly distributed. Then sprinkle the cheddar cheese evenly on top of that. Pour the egg mixture in last and make sure everything is even and submerged in the egg. Bake the quiche for 30 minutes for it to cook through and set. Let it cool for 15 minutes, then put the tart on top of a large can or container so that the tart pan edge slips right off to release the quiche. Slice it and serve immediately!