In a 9 x 13 dish whisk together the olive oil, soy sauce, minced garlic, cumin, oregano, paprika, and chili powder. Add the beaver steak, toss to coat well, and marinate for at least 4 hours or overnight.
When ready to cook the marinated beaver steak, pour 1 Tablespoon of canola oil into a large nonstick skillet and swirl to coat. Using tongs, gently lay beaver steak in skillet and cook over medium-high heat until underside is nicely browned, about 3 minutes.
Flip the beaver steak over, reduce heat to medium, and cook until reverse side is equally browned and steak is medium-rare (an instant-read thermometer inserted into the thickest part will register 130 degrees F), about another 3 minutes. Transfer steak to a cutting board to rest for about 10 minutes.
While the steak is resting, in the same large nonstick skillet over medium-high heat, add butter, bell pepper, onion, and hashbrowns, and sauté for about 5 minutes, stirring often.
Meanwhile, whisk the eggs in a small bowl.
Add eggs to the skillet, and cook until scrambled, then remove from heat.
Thinly slice cooked beaver steak with a sharp knife, cutting away from your body and with the top edge of the knife leaning toward your body. Make sure to slice across the grain of the meat.
Layout a large flour tortilla on a cleancutting board and spread ½ the sour cream evenly over one side. On the bottom ½ of the tortilla, add ½ the shredded cheese, ½ the scrambled egg mixture, ½ the sliced beaver steak, and ½ the Pico de Gallo and guacamole.
Fold the sides of the burrito over the filling and then roll the tortilla into a tight burrito. Repeat with the other tortilla and other ½ of the ingredients. Slice and serve.
If you are freezing the burritos, wrap each of them separately in aluminum foil before placing them in a freezer-safe resealable plastic bag. You can also use a vacuum seal bag here. Burritos will store well in the freezer for up to three months.