Bring a large pot of water to a boil over high heat. Add shrimp and 1 tablespoon salt; reduce heat to low and cook until shrimp are pink, about 2 minutes. Drain the shrimp and transfer to the bowl of cold water until chilled, 3 to 5 minutes. Drain again.
Combine remaining 1 tablespoon salt, lemon zest and juice, parsley, pickling spice, garlic, and red pepper flakes in a bowl. Pour in olive oil and whisk together to make the pickling oil.
Fill a resealable glass jar with shrimp and shallots in 4 alternating layers. Pour the pickling oil on top, submerging all contents. Put on the lid and refrigerate for 24 hours.