Preheat the broiler. Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs; drain.
Meanwhile, heat the vegetable oil in a large ovenproof skillet over medium-high heat. Add the onion, mushrooms and 2 teaspoons thyme. Cook, tossing occasionally, until tender and beginning to brown, 10 to 12 minutes; season with salt and pepper. Stir in the flour to coat the vegetables; cook 1 minute. Add the chicken broth and milk and bring to a boil, stirring, until the mixture is thick and creamy, about 3 minutes. Stir in the tuna and 1/2 cup pimiento cheese; stir until the cheese melts, about 2 minutes. Stir in the pasta until combined; season with salt and pepper.
Dollop the remaining 1/2 cup pimiento cheese on the pasta mixture and broil until the cheese is melted and browned in spots, 1 to 3 minutes. Sprinkle with the cracker crumbs and remaining 1 teaspoon thyme and broil until the crackers begin to brown, 30 seconds to 1 minute. Let cool 10 minutes.