Prepare a water bath canner and two pint jars and lids.
Wash and dry peppers and trim stems if necessary. Sort peppers into two bowls, one for larger-sized peppers and one for smaller peppers.
Heat a medium-sized cast-iron skillet on high. When the pan is hot, add a tablespoon or two of the oil and swirl to coat the bottom of the pan.
When the oil just begins to smoke, add one of the two bowls of peppers, taking care not to crowd them (you may need to do this in a few batches). Let the peppers cook for two to three minutes on high, checking the skins occasionally. When most of the peppers have blistered dark brown, flip and cook on high for another two minutes. Using tongs or a slotted spoon, put the peppers back in the empty bowl to cool. Repeat with the other bowl of peppers, then set aside to cool.
Put vinegar, water, and pickling salt in a small saucepan over high heat and bring to a boil.
Crush and peel garlic and add two cloves to each jar. Peel shallots, slice in half, and add two halves to each jar. Distribute peppercorns and a few springs of the basil evenly between the two jars.
Once peppers have cooled, pierce each one with a knife so that pickling liquid can penetrate. Pack the peppers into the jars — they should be pretty soft by this point and easy to pack tightly.
When brine has boiled, remove from heat and carefully pour over the peppers in the jars. Wipe rims, apply lids and rings, and process in water bath canner for 10 minutes.