Beat butter in the bowl of a standing electric mixer until light and fluffy. Slowly stir in sugar and then beat on high speed until well mixed, 2 to 3 minutes.
Add eggs, one at a time, beating thoroughly after each addition. Add flour, baking powder, cardamom, nutmeg, and salt. Stir to combine and then beat on high speed until the stiff batter is well blended, about 2 minutes.
Scrape batter into a buttered, flour-dusted 9-inch spring-form pan. Spread the thick batter evenly to the pan's edges. Arrange nectarines atop of the batter, spacing them as closely together as you can without overlapping them. Mix the remaining 1 tablespoon sugar with 1/8 teaspoon cardamom and sprinkle it evenly over the fruit.
Bake at 350° F on the oven's center rack until the cake begins to pull away from the pan rim, about 55 minutes. Run a thin metal spatula between the cake and pan rim. Allow to cool for at least 10 minutes before serving.
Remove cake from pan and serve with lightly sweetened whipped cream, if desired.