Cook chicken: Stovetop: bring large pot of water to a boil. Add chicken. Cook 20 min or until no longer pink. Shred chicken* and set aside.Instant Pot: add 1 cup water to the bottom of the insert. Add trivet. Place chicken on trivet. Lock lid; set valve to sealing. Program for poultry. Allow for NPR. Open lid, remove chicken, and shred with two forks*. Set aside.(*You can also shred chicken easily with a stand mixer.) Heat oil in a large skillet. Add diced onion and garlic. Cook, stirring occasionally, 5 minutes. Add chicken, beer, cayenne, and tomatoes. Cook until liquid evaporates, about 20 minutes. Stir in half the olives and half the green onions.
Preheat oven to 350.
Combine flour, salt, cumin, and coriander. Add mixture to a medium saucepan over medium heat. Slowly whisk in milk, a little at a time, incorporating each addition before adding more. Bring to a simmer, stirring frequently. When mixture thickens, remove from heat.
Spray 2.5 quart casserole dish with cooking spray. Add 1/2 cup flour mixture to the bottom of prepared dish. Top with 4 tortilla halves. Add 2 cups chicken mixture. Add about 1/2 -3/4 cup cheese.Add 1/2 cup flour mixture, 4 tortilla halves, and 2 cups chicken mixture. Top with 1/2-3/4 cup cheese.Repeat layers one more time, ending with flour mixture. Bake at 350 for 40 min. Remove from oven and top with remaining cheese, remaining olives, and remaining green onions. Let stand 5-10 min to melt the cheese topping. Serve with sour cream and salsa.