Make the pico de gallo first by combining all ingredients together in a bowl. Let sit at room temperature while you prepare the rest.

Cook chorizo in a skillet over medium heat until browned. Remove from heat. Cover to keep warm.

Heat oil in a skillet over medium heat. Cook gyoza one at a time 10 seconds on each side. Use tongs to pick up the wonton and pinch to fold but don't close completely. Transfer to a paper towel lined plate. Sprinkle with salt. Repeat until all wonton skins are fried.

Fill each wonton shell with a heaping of tablespoon chorizo. Top with pico de gallo and cotija cheese.