Adjust oven rack to middle position and heat oven to 350 degrees.
Melt 3 tablespoons unsalted butter in Dutch oven over medium-high heat.
Add 2 finely chopped onions and cook until softened, about 5 minutes.
Add ¼ cup all-purpose flour and cook, stirring constantly, until golden, about 1 minute.
Slowly whisk in 1½ cups chicken broth, 1 cup half-and-half, 1¾ teaspoons table salt, ½ teaspoon dried thyme, and ¼ teaspoon pepper and bring to boil.
Reduce heat to medium-low and simmer, stirring occasionally, until slightly thickened, 3 to 5 minutes.
Off heat, whisk in 2 cups shredded sharp cheddar cheese until smooth.
Stir 8 cups frozen shredded hash brown potatoes into sauce, cover, and cook, stirring occasionally, over low heat until thawed, about 10 minutes.
Off heat, stir in ½ cup sour cream until combined.
Scrape mixture into 13 by 9-inch baking dish and top with 4 cups sour-cream-and-onion potato chips, crushed.
Bake until golden brown, 45 to 50 minutes.
Let cool 10 minutes. Serve.
Potato mixture can be refrigerated in baking dish, covered with aluminum foil, for 2 days.
To finish, bake potatoes 20 minutes. Remove dish from oven and uncover. Top with potato chips and bake until golden brown, 45 to 50 minutes.
