Heat 1 tablespoon olive oil over medium-high heat in a large nonstick skillet. Add the potatoes and yellow onion and cook, stirring occasionally, for about 15-20 minutes, until the potatoes are tender and the onions are golden brown. Season well with salt and pepper, and set aside in a medium bowl.
Next, add the tomatillos, white onion, jalapeño, garlic, and cilantro to a high-powered blender. Blend on medium speed until the mixture is roughly chopped and evenly combined. Don’t blend it too long, or the salsa will be too thin and watery.
Crack the 10 large eggs into a medium bowl and beat with a fork or whisk. Stir in the butter and half and half and season with salt and pepper. Pour the eggs into a medium nonstick skillet and scramble over medium heat with a spatula. When the eggs are scrambled to your liking, turn off the heat and put the eggs in small bowl.
To assemble the burritos, lay out a sheet of foil and place a tortilla in the center. Place a couple slices of avocado on the bottom third of the burrito. Top with a spoonful of potatoes, a spoonful of eggs, a spoonful of salsa (if you’re freezing the burritos, press some of the liquid out of the salsa first to avoid soggy burritos), and a generous sprinkle of cheese. Roll up like a burrito and wrap with foil before placing in the freezer. You might have leftover filling ingredients, and that’s totally fine! The leftovers make a great easy breakfast the next day.
When you’re ready to eat one of the frozen burritos, unwrap it from the foil and throw the foil away. Wrap the burrito loosely with a moistened paper towel and microwave for 1 1/2 to 2 minutes until defrosted and heated to your liking. Enjoy with extra salsa on the side.