Pimento cheese on a hot dog is nothing short of genius. Allowing pickled jalapeños to sit in sugar overnight tames the peppers' heat, while intensifying their sweetness. This spiciness is the perfect contrast to the rich pimento cheese.
Drain liquid from pickled jalapeño chile slices. Add lime zest and 1/4 cup sugar to jalapeño slices in jar. Screw lid on jar, and shake to coat jalapeños. Remove lid; add 1/4 cup sugar. Screw lid on jar, and shake to coat. Repeat process with remaining 1/4 cup sugar. Chill 24 hours to 1 week, shaking jar several times a day to disperse any sugar that may settle.
Stir together mayonnaise, diced pimientos, and crushed red pepper in a large bowl. Shred sharp Cheddar cheese using the large holes of a box grater and white extra-sharp Cheddar cheese using the small holes of a box grater. Gradually stir shredded cheeses into the mayonnaise mixture. Cover and chill until ready to use.
Preheat grill to medium-high (350°F to 400°F). Grill hot dogs about 6 minutes, turning occasionally, until heated through and grill marks appear. Grill buns, if desired. Place hot dogs in buns. Top each with about 2 tablespoons pimiento cheese and a few drained jalapeños.