For the cilantro chutney: Put the cilantro, lime juice, agave, scallions, chile, 3/4 teaspoon salt and 1 tablespoon water in a blender. Blend on high, scraping down the sides with a rubber spatula as needed, until almost smooth with some specks of herbs remaining. Set aside until ready to serve.
For the chorizo in a blanket: Heat 1 tablespoon oil in a small skillet over medium-high heat. Add the chorizo and cook, breaking up the meat into small pieces with a wooden spoon, until golden brown in spots and no longer pink, about 5 minutes. Set aside to cool.
Fill a large heavy-bottomed pot with enough oil to reach 2 inches up the side. Heat over medium-high heat until the oil reaches 350 degrees F on a deep-fry thermometer.
Use a 2 3/4-inch square cutter to press out 18 squares of empanada dough (2 squares per sheet of dough). Cover with a damp paper towel to prevent the dough from drying out. Place 1 heaping teaspoon each of chorizo and cheese in the center of each square of dough. Brush the edges with a small amount of water, then fold the dough over the filling and press to seal. Use a fork to securely seal the edges.
Deep-fry the chorizo in a blanket in 2 batches, flipping and turning with a slotted spoon as needed, until puffed and golden brown, about 5 minutes. Drain on a paper towel-lined baking sheet and sprinkle with salt. Serve with the cilantro chutney for dipping.