Preheat oven to 425°F. Line two sheet pans with parchment and lightly oil.
Warm tortillas until pliable. Microwave wrapped in a damp towel for 45 seconds or briefly toast on a dry skillet.
Stir together chicken, cream cheese, Monterey Jack, green chiles, lime juice, chili powder, cumin, garlic powder, onion powder, salt, pepper, and cilantro.
Spread about 2 tablespoons filling along the lower third of a warm tortilla.
Roll tightly into a thin cigar and place seam-side down on the pan.
Repeat with remaining tortillas and filling, spacing taquitos slightly apart.
Brush taquitos lightly with the remaining oil.
Bake 14–18 minutes until crisp and golden, rotating pans once. Let rest 2 minutes before serving.