Heat a large skillet over medium heat and add the ground beef, chopped onion, and diced jalapeños; cook until the beef is browned and onions are softened, about 6–8 minutes.
Add the minced garlic and sauté for about 30 seconds until fragrant, then drain any excess fat from the pan.
Stir in chili powder, cumin, smoked paprika, salt, and dried oregano until evenly combined with the meat.
Reduce heat to medium-low and add the cream cheese and salsa; stir frequently until the cream cheese is fully melted and the mixture is smooth.
Stir in 1 cup of the grated Pepper Jack cheese until melted, then remove the filling from heat and let it cool slightly.
To assemble, place a tortilla flat and spoon a heaping 1/4 cup of filling across the bottom third of the tortilla, then top with about 1 tablespoon of the remaining Pepper Jack cheese and roll tightly.
Heat 1 teaspoon olive oil in a large nonstick skillet over medium heat. Working in batches, place rolled taquitos seam-side down and cook, turning as needed, until golden brown and crisp on all sides, about 2–3 minutes per side.
Transfer cooked taquitos to a plate lined with paper towels briefly to drain any excess oil, then serve warm.