Toss the shallots with 1/4 cup half-and-half and a large pinch each of salt and black pepper in a small bowl. Set aside to soak 10 minutes.
Meanwhile, combine the flour, cayenne, 1/2 teaspoon salt and a few grinds of black pepper in a medium bowl. Heat about 1/4-inch vegetable oil in a medium nonstick skillet over medium heat. Working in batches, remove the shallots from the half-and-half, coat with the seasoned flour and fry, stirring, until crisp and golden brown, 4 to 6 minutes. Remove with a slotted spoon to a paper towel-lined baking sheet to drain; sprinkle with salt. Add more oil to the skillet as needed between batches.
Bring a medium saucepan of salted water to a boil. Add the peas and cook until tender, 5 to 7 minutes; drain. Add the remaining 3/4 cup half-and-half and the cheese to the pan and cook over medium-low heat, stirring, until creamy. Stir in the lemon zest, nutmeg and a few grinds of black pepper. Stir in the peas until well coated; season with salt and black pepper.
Remove the pan from the heat and stir in the parsley. Transfer to a serving dish and top with the fried shallots.
Make the creamed peas (step 3) up to 1 day ahead; cover and refrigerate. Reheat over low heat, adding 1 to 2 tablespoons more half-and-half to thin the sauce, then stir in the parsley. Fry the shallots before serving.