Split the shrimp down the back with a paring knife, and devein. Cut almost all the way through the shrimp to butterfly them open, but leave the shells on.

Toss the shrimp in a large bowl with the thyme, ¼ cup of the olive oil, four of the crushed garlic cloves, ¼ teaspoon of the salt, and the crushed red pepper. Marinate in the refrigerator for 1 hour.

Meanwhile, in a food processor, combine the arugula, remaining two garlic cloves, and remaining ½ teaspoon salt. With the machine running, drizzle in the remaining ½ cup olive oil to make a smooth, thick sauce. Pour into a bowl, and set aside.

When you are ready to cook the shrimp, heat a large nonstick skillet over high heat. Remove the shrimp from marinade, and add in batches, butterflied side down, until they are cooked through and just begin to pull away from the shell, about 2 to 3 minutes per batch. Add the shrimp to a large bowl, and repeat with the remaining shrimp.

When all of the shrimp are cooked, add about half of the sauce to the bowl with the shrimp and toss well. Mound the shrimp on a serving platter, and serve with the remaining sauce on the side for dipping.