For the dressing, Blend the first seven ingredients (pepperoncini juice through oregano) in a blender and set aside.
For the yogurt sauce, mix together the remaining ingredients and set aside.
For the gyro dogs:
Heat a grill pan over a medium-high flame. Grill the hot dogs, turning every couple of minutes, until evenly covered with grill marks. While the hot dogs cook, toss the lettuce, tomatoes, onion, cucumber, feta, pepperoncini, and olives with the dressing. To serve, slather a piece of bread with yogurt sauce. Lay over the hot dog and top with dressed salad. A fresh lemon wedge is nice on the side.