1. In a small saucepan set over high heat, bring the vinegar, garlic, orange peel, salt and sugar to a boil. Place the jalapeños in a small bowl. Strain the pickling mixture through a fine-mesh sieve and over the jalapeños, then cool to room temperature. Transfer to an airtight container and refrigerate overnight.

2. Preheat the oven to 175°. Drain the jalapeños and place them and the Thai basil leaves in a single layer on a rimmed baking sheet. Place in the oven and dehydrate until the leaves and jalapeños are completely brittle and dry, about 2 hours. Remove from the oven and add to a food processor along with the crackers, Parmigiano-Reggiano, sea salt and dried chile(s). Pulse until very fine. Transfer to a pizza-parlor-style cheese shaker and sprinkle over pizza.