Blistered Cheesy Peppers

Ingredients

• large shallot, halved, thinly sliced lengthwise
• red wine vinegar
• sugar
• kosher salt, plus more
• extra-virgin olive oil, divided
• large poblano chiles or 3 large Cubanelle peppers or Anaheim chiles , cut in hal
• Freshly ground black pepper
• pepper Jack, cut into ½" cubes
• garlic cloves