Thaw the frozen shrimp (at room temperature or under running cold water). Rinse and remove the tails, dry them.
Grate or press one clove of garlic through a garlic press, cut the second one into thin slices. Cut the chili pepper diagonally into thin slices.
Arrange the lettuce on plates, sprinkle with arugula, place halved or quartered cherry tomatoes on top.
In a pan melt butter with olive oil and once it starts sizzling add the garlic slices, shrimp and chili pepper. Fry over slightly higher heat for about one minute on each side, seasoning with salt along the way.
Then add the grated garlic, mix and fry for half a minute, stirring occasionally. Pour in the wine and lemon juice, mix and remove from the heat. Place on the lettuce. You can drizzle with additional olive oil.