Shred the chicken: Pull the rotisserie bird apart with two forks while it’s still warm, working into bite-size shreds. You want about 3 heaping cups a little more is never a complaint.
Make the filling thick on purpose: In a bowl, beat half the cream cheese with the ½ cup of sour cream and the ranch packet until smooth no white lumps allowed, so let the cream cheese genuinely soften first. Fold in the shredded chicken, the 1 cup of cheese, and the green chiles if using. This is where the ratio decides everything: the filling should be scoopable paste, the kind that holds its shape on the back of a spoon. If it looks like it could pour, that’s the sign and the danger. A pourable filling finds its way out of the tortillas by the second minute in the oven and pools in the dish. Keep it dry; the sauce has all the liquid duties around here.
Make the creamy sauce: In a small saucepan over low heat, whisk the remaining cream cheese, the ⅓ cup sour cream, and the milk until smooth and warm. Whisk in the green enchilada sauce and let it come together for 2–3 minutes barely a simmer. Gentle heat and a busy whisk keep the dairy from splitting into streaks; this sauce is meant to bake glossy, not broken.
Warm the tortillas: Heat each tortilla in a dry skillet for about 10–15 seconds per side, just until pliable and faintly blistered. Stack them on a plate under a towel. Pro tip: a shy warm-up does three jobs the tortillas roll without cracking, they hold their shape under the sauce, and they don’t soak up the liquid the way cold, raw tortillas do.
Coat the dish: Spread about ½ cup of the sauce across the bottom of the 9×13. This under-sauce layer keeps the rolls from sticking and keeps their undersides moist skip it and the first roll sticks, the last one steams, and everyone’s got a favorite corner that nobody asked for.
Assemble the rolls: Spoon a generous line of filling down the center of each tortilla, roll snugly, and place seam-side down in the dish. Nestle them close so they hold one another up; eight rolls in one snug layer is the goal.
Top and bake covered first: Pour the remaining sauce over the rolls, ease it into every gap with a spatula, and scatter the 1½ cups of cheese over everything. Cover with foil and bake at 375°F for 15 minutes the covered start heats the filling through and lets the sauce marry into the rolls without scorching the cheese. Then uncover and bake 10–12 minutes more, until the sauce bubbles at the edges and the cheese is molten with a few blistered spots.
Rest before serving: Let the dish stand for a solid 10 minutes once it’s out. Clean slices come from patience, plus it gives the creamy sauce a beat to settle instead of running across the plate.
