Prepare an ice water bath; set aside. Line a baking sheet with a cooling rack; set aside.

Bring a large pot of water to a boil. Add a generous amount of salt and the peas. Cook until bright green, 3 to 4 minutes. Using a slotted spoon, transfer to ice water bath to stop the peas from cooking. Drain, shaking off excess liquid; set aside. Add the spinach to the boiling water and cook, just until wilted, about 1 minute. Drain, squeezing out excess moisture, and transfer to wire rack to dry.

Heat the oil in a large skillet over high heat. Add the shallots and cook, stirring frequently, until translucent, but not brown, about 2 minutes. Stir in peas, and cook 1 minute. Add the spinach, tossing to combine, and heat through, 1 to 2 minutes more. Season with salt and pepper. Serve immediately.