Preheat the oven to 350ºF and generously butter a 9x13 pan. Halve the nectarines, discard the pits and cut into thin slices—say 8 per nectarine. Leave on the skin. Arrange the slices in the buttered pan in a single layer.
Break the 5 eggs into a large bowl. Add the vanilla, almond extract, sugar, cardamom or nutmeg, and salt. Whisk together until everything is well blended.
Stir in the whole milk and melted butter, then the flour. When everything is smooth, pour over the nectarine slices. Slide into the oven and set a timer for 50 minutes.
After 25 minutes, turn the pan around for even baking. Bake another 25 minutes, until it is barely set, a bit puffy, and the edges are starting to turn golden. It really is OK if the very center is still a bit wobbly—overbaking will make your clafoutis rubbery.
Cool on a rack for 15 or 20 minutes, then serve warm, cut into squares. This is wonderful on its own; if you are in a fancy mood, add a small scoop of vanilla or caramel ice cream, or some whipped cream. This is also lovely the next day, at room temperature, and even cold, with a nice hot cup of coffee.