In a shallow dish, whisk together the eggs and mustard until smooth. In a separate shallow dish, combine the pretzels and thyme.
Dip the chicken in the egg mixture, letting the excess drip off. Dredge in the pretzel mixture to coat.
In a large nonstick skillet, heat 2 tablespoons of the olive oil over medium heat. Add half of the chicken and cook until cooked through, 5 to 6 minutes per side. Remove the chicken from the skillet and keep warm. Repeat the procedure with the remaining 2 tablespoons oil and chicken. Wipe the skillet clean.
Melt the butter in the skillet over medium heat. Add the flour and cook, whisking constantly, for 2 minutes. Slowly add the milk, whisking until smooth. Cook, whisking constantly, until thickened and bubbly, 6 to 8 minutes. Add the cheese and stir until the cheese melts and the sauce is smooth.
Spoon the sauce over the chicken. Serve with Broccoli and Rice Pilaf.
In a medium saucepan, melt the butter over medium heat. Add onions and cook, stirring frequently, for 3 minutes. Add the broccoli and cook for another 3 minutes. Add the rice and cook, stirring constantly, for 1 minute. Stir in the broth. Increase the heat to medium-high and bring the mixture to a boil. Cover, reduce the heat and simmer until the rice is tender, 15 to 20 minutes.