For the pico de gallo: Mix together the red onions, tomatoes, jalapenos and cilantro in a bowl. Add the lime juice and salt and black pepper to taste. Let stand for 1 hour. Drain, reserving 1 1/2 cups of accumulated liquid.
For the bison: Heat a skillet over high heat, and then add the bison and Spanish onions and cook until browned, 5 minutes. Add the vinegar, olive oil, cayenne, coriander, cumin, salt, red pepper flakes and lime juice and cook for another 5 minutes. Drain and let cool, then fold in the cilantro. Refrigerate for 1 hour.
Fill a pot halfway with oil and heat to 350 degrees F.
For cooking the empanadas: Lay out the dough on a flat surface, and scoop 2 ounces of bison filling into the center of each piece of dough. Fold the sides closed, pressing to seal. Drop into the oil and fry for 2 minutes, frying in batches if needed.
Garnish the empanadas with the avocado jalapeno puree and top with the pico de gallo.