Trim the mushrooms and cut or tear into 1/2-inch pieces. Heat the olive oil in a large skillet over medium-high heat and cook the jalapenos, garlic and shallots until soft, about 2 minutes. Add the mushrooms and 1/2 teaspoon salt and cook, stirring occasionally, until the mushrooms release most of their liquid and are tender and browned in places, about 8 minutes. Remove from the heat, stir in the cilantro and lime juice and season with salt and pepper.
Lay out the empanada rounds and fill each with 2 tablespoons of the mushrooms. Brush the edge of the rounds with water, and then fold the circles in half. Crimp the edges tightly with a fork, to seal. Refrigerate until ready to fry.
Heat 1 1/2 inches of oil in a medium pot to 375 degrees F. Working in batches of 2 or 3, fry the empanadas until crisp and golden brown, 2 to 3 minutes per batch. Transfer immediately to a paper towel-lined plate to drain. Return the oil to 375 degrees F between batches.
Cook's Notes: The empanadas can be fried up to 3 hours ahead and kept at room temperature. Before serving, reheat on a baking sheet in a 375 degree F oven 15 minutes.
Cook's Note: The empanadas can also be formed up to 2 days ahead and kept frozen until ready to use. No need to thaw before frying.