Combine the vinegar, water, salt, sugar, coriander seeds, peppercorns, garlic, jalapeños, and dill in a medium saucepan over medium-high heat. Bring to a boil.
Place the sliced cucumbers in a small heatproof bowl. Pour the boiling liquid over the cucumbers to submerge. Let stand at room temperature for 1 hour. Drain the pickles. If you don’t plan on using all of the pickles, reserve the pickling liquid so that you can keep the leftover pickles in their liquid in the refrigerator.
Place a griddle over medium heat. Place the bottom halves of the rolls on a clean work surface. Spread 1 teaspoon of mustard over the bottom of each roll. Divide the arugula, pickles, ham, and pawlet cheese between the bread and place the tops over the sandwiches. Grill the sandwiches for 2 to 3 minutes per side, until the bread is golden brown and the cheese is melted. Transfer the sandwiches to a cutting board. Cut each sandwich in half and serve.