Heat 2 tbsp. oil in large saucepan over medium-high heat until shimmering. Add garlic and red pepper flakes for about 30 seconds. Add beans, bring to a boil, then reduce it to a simmer for about 15 minutes. Season with salt and pepper.
To make pico de gallo, (a Mexican fresh, uncooked salad made from chopped tomato, white onion, and chilis, generally jalapeños or serranos), combine 2 tbsp. cilantro, tomatoes, onion, jalapeno, and lime juice in medium bowl. Season with salt and pepper.
Slice hindquarter venison in half horizontally. Pound each half to about 3/4 inches thick. Season liberally with salt and pepper. Heat remaining oil in a large skillet over medium high heat until skillet is smoking hot. Place venison in skillet for about 4 minutes on the first side, turn and cook the other side for 3 to 4 minutes. Transfer to a cutting board, tent with foil, and let rest 5 minutes.
For Tomatillo Sauce, saute onion in olive oil. Add tomatillos, chiles, and garlic Saute gently. Add the ingredients to a food processor. Add sour cream and cilantro. Process until smooth. Add whipping cream and pulse until blended.
Slice steaks thin against grain. Place tortillas on 4 plates and evenly divide rice, beans, venison, and pico de gallo among them. Spoon tomatillo sauce on top. Fold tortillas to form burritos. Sprinkle remaining cilantro leaves on top and serve immediately.