How to Make It
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.