Season all sides of the halibut with the 1 teaspoon of salt and 1 teaspoon of pepper. In a shallow dish, combine the flour and the remaining salt and pepper. In a second shallow dish add the eggs. Add the pepitas to a third shallow dish. Roll a halibut fillet in the flour, shaking off the excess. Dip just 1 side of the fillet in the beaten eggs, then into the pepitas, pressing gently for even coverage. Set on a plate, seed side up, and repeat with remaining halibut. Cover loosely and refrigerate for 15 minutes.
While the fish is resting, prepare the cilantro cream.
Preheat the oven to 300 degrees F.
Heat a nonstick skillet over medium-high heat and add the canola oil. When the oil is hot add the fish, pepita side down, and cook until golden, about 2 minutes. Flip over, then gently transfer them to a baking sheet fitted with a rack. Bake in the oven until the internal temperature of 145 degrees F registers on an instant-read thermometer, about 6 to 7 minutes. Arrange on serving plates, topped with the cilantro cream and serve.
Melt the butter in a small saucepan over medium-high heat. Add the shallot and serrano pepper and saute for 1 minute. Add the half-and-half and cilantro and bring to a low simmer. Stir frequently until reduced by half, about 6 to 8 minutes. Remove from the heat, stir in the lime juice and salt and blend with a stick blender until smooth, Keep warm, or reheat gently before serving.