Heat a large skillet over medium-high heat and add 1 tablespoon of vegetable oil. When shimmering, add the hash browns in an even layer; season lightly with Kosher salt and black pepper. Cook, stirring occasionally, until golden and crispy, about 8–10 minutes. Transfer to a plate and keep warm.
In the same skillet, add another drizzle of vegetable oil and crumble in the breakfast sausage. Cook, breaking up the meat, until browned and cooked through, about 6–8 minutes. Transfer the cooked sausage to the plate with the hash browns.
Add the diced onion and bell pepper to the skillet and sauté until softened and slightly caramelized, about 5–7 minutes. Stir in the garlic and cook until fragrant, about 30 seconds.
Return the sausage and hash browns to the skillet with the vegetables, toss to combine, and adjust seasoning with more Kosher salt and black pepper to taste. Keep the filling warm while you make the eggs.
Whisk the eggs with a pinch of Kosher salt and black pepper. Melt 1 tablespoon of butter in a clean nonstick skillet over medium-low heat, pour in the eggs, and gently scramble until just set but still moist. Remove from heat.
Warm the flour tortillas in a dry skillet or wrapped in a damp towel in the microwave for a few seconds until pliable. Lay a tortilla flat, layer with a scoop of the potato-sausage-veg mixture, some scrambled eggs, and a sprinkle of cheddar cheese.
Fold the sides of the tortilla in, then roll tightly from the bottom to form a burrito. Repeat with remaining tortillas and filling. If desired, toast the burritos seam-side down in a hot skillet for 1–2 minutes per side to seal and crisp the exterior.
Serve the burritos with salsa and hot sauce on the side for spooning or drizzling. Enjoy hot.
