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In a large non-stick skillet, melt the butter over a high heat with the olive oil and thyme. When the butter starts to foam, add the tomatoes and sauté until they begin to wilt, about 2 minutes.
Add the olives, seafood mix and salt to the pan, cover with a tight-fitting lid and cook until the seafood is done but still tender, about 5 minutes. Make sure not to overcook or it will become tough and rubbery. The seafood should still have a lot of cooking juices, and that is okay, as you will use them instead of a dressing.
Divide the arugula into four serving bowls and pour some of the seafood mix on each. Serve immediately.
You can use a baby greens mix instead of arugula, or use your favourite lettuce. Romaine is a great fit for this recipe.