Pour olive oil into a large soup pot, place over high heat, add spinach, and cover. Cook for 1 minute, uncover, and lightly stir until most of the leaves are bright green and wilted, about 2 minutes. Quickly drain spinach in a strainer and transfer to a plate lined with 4 or 5 paper towels. Once cool enough to handle, squeeze as much liquid from the spinach as possible. Transfer spinach to a cutting board and coarsely chop.
Mix salt, black pepper, cayenne pepper, and nutmeg in a small bowl.
Place a large skillet over medium heat, melt butter in skillet, and stir shallot in the hot butter until just barely golden and translucent, 3 to 4 minutes. Stir seasoning mixture into shallot mixture and pour in cream. Raise heat to medium-high and reduce cream sauce to about half, about 5 minutes. Stir in lemon zest.
Reduce heat to low and toss spinach with cream sauce in skillet. Cook and stir until spinach is heated through and coated, about 2 minutes. Stir Parmigiano-Reggiano cheese into spinach until thoroughly combined; serve immediately.