Wilt 1 lb. spinach at a time in a large pot of boiling water, stirring often, 1 minute. Transfer to ice water, then to a colander.
Heat 2 in. vegetable oil in a medium saucepan over medium heat. In a bowl, toss shallots with flour until lightly coated. To test oil, throw 1 shallot slice in pan; it should sizzle and bubble to the top but not turn golden right away. Fry small batches of shallots, stirring often, until golden, 2 to 3 minutes. Drain on paper towels.
Pat excess moisture from spinach. In a large frying pan, sauté spinach, salt, and pepper in 1 tbsp. olive oil over high heat, tossing with tongs, until spinach is hot and some liquid evaporates, 7 minutes.
Remove spinach from heat, drain off liquid, and stir in remaining 2 tbsp. olive oil. Transfer to a dish. Top with shallots.
Make ahead: Up to 1 day ahead, prepare spinach through step 1; cover colander, set in a bowl, and chill. Shallots can be fried 6 hours ahead and stored between paper towels.
Note: Nutritional analysis is per serving.