Arrange a rack in the middle of the oven and heat the oven to 350°F.
Shred 1 pound cooked boneless, skinless chicken into bite-size pieces (about 4 cups), and place in a 9x13-inch baking dish. Add 1 (10 ½-ounce) can condensed cream of chicken soup, 1 ½ cups sour cream, 2 teaspoons of the poppy seeds, ½ teaspoon black pepper, and ¼ teaspoon kosher salt. Stir to combine and spread into an even layer. Wipe down the sides of the baking dish with a damp paper towel to clean it off if desired.
Cut 6 tablespoons unsalted butter into 6 pieces and place a medium microwave-safe bowl. Microwave until almost completely melted, 40 to 60 seconds (alternatively, melt on the stovetop and transfer to a medium bowl).
Place 45 Ritz crackers in a large zip-top plastic bag and seal the bag. Use your hands to crush into coarse crumbs (about 2 cups). Add the crackers and remaining 1 teaspoon poppy seeds to the butter and stir to coat. Evenly sprinkle the cracker crumbs over the top of the casserole.
Bake until the edges are bubbling and the top is golden-brown, 30 to 40 minutes. Check after 25 minutes and cover with aluminum foil if the crackers brown too quickly. Let cool for 5 minutes before serving.
