Bake the Tater Tots® until very crispy, following the package directions.
Meanwhile, combine the half-and-half, 1 cup of the cheese, and the cornstarch in a small saucepan. Whisking constantly, cook over medium heat until melted and smooth, 3 to 4 minutes. Stir in the pico de gallo.
When the Tater Tots are done, transfer them an 8-inch cast-iron skillet. Preheat the broiler to high. Spoon the cheese sauce over the tots and sprinkle with the remaining 1/4 cup cheese. Broil until the cheese is bubbling and melted, about 1 minute. Top with the cilantro and a dollop of sour cream.