Adjust oven rack to upper-middle position, about 5 inches from heating element; heat broiler. Whisk eggs, half-and-half, 1/2 teaspoons salt, 1/4 teaspoons pepper in medium bowl until well combinedm about 30 seconds. Set aside eggs.
Heat butter in 12-inch nonstick ovensafe skillet over medium heat until foaming subsides. Add leeks and 1/4 teaspoons salt; reduce heat to low and cook covered, stirring occasionally, until softened, 8-10 minutes. Stir prosciutto, basil, and half of goat cheese into eggs; add egg mixture to skillet and cook, using spatula to stir and scrape bottom of skillet, until large curds form and spatula begins to leave wake but eggs are still very wet, about 2 minutes. Shake skillet to distribute eggs evenly; cook without stirring for 30 seconds to let bottom set.
Distribute remaining goat cheese evenly over frittata. Slide skillet under broiler and broil until frittata has risen and surface is puffed and spotty brown, 3-4 minutes; when cut with a paring knife, eggs should be slightly wet and runny. Remove skillet from oven and let stand 5 minutes to finish cooking; using spatula, loosen from skillet and slide onto platter or cutting board. Cut into wedges and serve.