Pat the chicken dry and season both sides with salt, pepper, and garlic powder.
Make the pretzel crumbs. Transfer the pretzels to a blender or a food processor. Quickly pulse the pretzels until you have a mixture of about 80% fine crumbs and 20% chunky pretzel pieces.
Pour the ½ cup of flour out onto a large plate or into a shallow bowl. Crack both eggs into a shallow bowl and whisk until combined. Pour the pretzel crumbs onto a large plate or into a shallow bowl.
Bread the chicken. Press both sides of each chicken cutlet into the flour. Submerge the chicken into the eggs to coat. Press both sides of the chicken into the pretzel crumbs. Repeat this process for each piece of chicken.
Pour the olive oil into a large, heavy-duty skillet and warm over medium heat. When the oil is hot, place the chicken pieces in the pan in a single layer. Do not crowd the pan. You may need to pan-fry your chicken pieces in batches.
Pan-fry over medium heat for 5 minutes. Flip the chicken over and fry for an additional 3-5 minutes, or until the chicken is cooked through. If the oil starts to get too hot, adjust your burner heat as needed. You may need to add additional tablespoons of cooking oil to your pan so that your skillet stays well-oiled!
While the chicken is cooking, make the blue cheese sauce. Melt the butter in a small saucepan over low heat. Once the butter is melted, whisk in the 2 tablespoons of all-purpose flour. Whisk the flour and butter until a paste forms. The paste will be smooth and light brown. Pour in the milk. Increase the heat to medium and rapidly whisk the mixture. Continue whisking until the butter, flour, and milk have thickened. You will know when the sauce has thickened when it coats the sides of the saucepan.
After the mixture has thickened, turn the heat back down to low and add in the crumbly blue cheese. Whisk in the cheese until melted. Remove the saucepan from the heat and set aside.
Let the cooked chicken rest for about 5 minutes before slicing. Serve with warm blue cheese sauce drizzled on top.