Preheat the oven to 400°F (200°C).
Arrange the turkey ham slices on a baking tray and bake for about 15–18 minutes until lightly crisp. Transfer to a paper towel-lined plate.
Heat the neutral oil in a skillet over medium-low heat. Add the frozen hash browns, pressing them into an even layer. Cook for about 5 minutes per side until crispy and golden. Remove and wipe the skillet clean.
Melt the butter in a nonstick skillet over medium-low heat.
Whisk the eggs with kosher salt. Pour into the skillet and gently scramble until just set.
Lay one tortilla flat. Sprinkle a little shredded cheese near the bottom, leaving a border around the edges.
Add half of the crispy hash browns, scrambled eggs, turkey ham, salsa (draining excess liquid), pickled jalapeños, avocado slices, and more cheese.
Fold in the sides and roll tightly into a burrito.
Repeat with the second tortilla.
Heat a skillet over medium heat. Sprinkle a little cheese directly onto the skillet and place the Breakfast Burritos seam-side down over the cheese. Cook until the cheese becomes golden and crispy, about 2 minutes.
Flip and repeat on the other side.
Slice in half and serve immediately with extra salsa.