Preheat the broiler to high.
In a medium bowl, whisk the eggs and cream together until completely smooth. Set aside.
Heat an ovenproof 10-inch skillet over medium-high heat. Add the oil; heat for a few seconds. Add the fennel and shallots; cook until the fennel has softened, 3 minutes. Season with the salt and add the tomatoes and trout; cook for another minute. Pour the egg mixture over the trout and let cook undisturbed for 1 minute. Using a rubber spatula, lightly scrape the bottom of the pan to bring up some of the cooked egg. Repeat 3 times. Evenly spread the mixture in the pan--the top will still be liquid--and dot the top with the basil and goat cheese.
Broil until the frittata is cooked through and lightly browned on top, 3 to 4 minutes. Let cool slightly before slicing and serving.