Melt butter and add 1 tablespoon of olive oil, the thyme, garlic, and hot sauce. Pulse giardiniera and olives in a food processor until finely diced. Add in 2 tablespoons of olive oil and pulse again until all the tiny bits just come together. Alternatively, you can chop this by hand and stir in the olive oil instead. Combine mayo and parsley.

Heat a saute pan over medium high heat. Add a small drizzle of oil - just enough so the fish won't stick. Add the fish and the butter mixture. Cook 3-4 minutes per side, or until the fish is opaque and cooked through. Be sure to baste the filets with the butter as they cook. Once the fish is done, assemble each sandwich by dividing all the components between the two sandwiches. Grab a napkin and enjoy!