Note: This recipe is a cinch, but you need an electric burner and a tart pan that you can use on the stove top (a metal pan is just fine - don't try this with a Pyrex or a ceramic dish). If you don't have an electric burner you can use a heat diffuser between a gas flame and the baking dish.
Heavily coat the bottom and sides of a 9 inch round metal tart pan with two tablespoons of the butter. Sprinkle the pan evenly with the sugar. Place the apricots with their skin side down in the pan. They should all be in one layer and nicely crowded.
Place the pan on a preheated (low to medium heat) electric burner. The sugar well melt and begin to caramelize. Remove the pan when it has turned lightly brown everywhere. This takes between 10 and 15 minutes.
Allow the pan to cool enough so you can touch it (always be very careful with hot sugar), then dot the fruit with the remainig tablespoon of butter cut into small pieces. Place the pie crust on top, tucking in the edges around the fruit. Prick several times with a fork, then bake at 400 degrees F for 20 minutes.
Allow to cool for 10 minutes before flipping. Depending on the apricots, this is likely to be a bit runny, but no worries, it is absolutely delicious. Serve with vanilla ice cream (not too French, but oh so good.)
Makes 6 servings.