Heat 1/4 inch vegetable oil in a small saute pan over medium heat until shimmering. Working in 3 batches, fry shallots, stirring occasionally, until golden brown, about 2 minutes. Transfer to a paper-towel-lined plate to drain, and season with 1/4 teaspoon salt.
Heat olive oil and garlic in a large saute pan over medium heat. Cook, stirring occasionally, until garlic turns golden brown, about 5 minutes. Remove and discard garlic. Add red-pepper flakes to pan, and cook 15 seconds. Fill pan with escarole, and cook, carefully stirring and adding more escarole, a handful at a time, as space allows. Once all of the escarole is in the pan, season with remaining teaspoon salt, and stir just until escarole begins to wilt and turn a vibrant green. Remove from heat, transfer to a serving dish, and top with fried shallots. Shallots can be fried up to 2 days ahead and stored in an airtight container at room temperature.