In a large bowl whisk together the eggs, heavy cream, salt, and pepper, and just until the egg yolks and whites have combined. Stir in half (1/4 cup) of the goat cheese
Place zucchini in clean kitchen towels and ring out as much liquid as possible.
Heat oil in a 12", oven safe skillet over medium. Once shimmering, add the zucchini and shallots and saute until the shallots are translucent about 4 minutes.
Stir the eggs one more time to incorporate everything that has settled, then pour it over the veggies. Use a spatula to spread the vegetables evenly across the bottom of the pan.
Reduce heat to low and place a lid on top. Continue to cook this way for 11-14 minutes, or until your frittata has set around the edges, but has a few areas that still jiggle.
Adjust the top rack of your oven so it is 8" from the heating element. Turn your broiler to high. Sprinkle the remaining 1/4 cup of goat cheese on top, and place your frittata in the oven, and continue to cook for 3-4 minutes, until the center is set and the top is golden.