Pat your shrimp dry with a paper towel and season lightly with sea salt and pepper on both sides.
Heat the oil and melt the butter in a large skillet over medium heat.
Cook your shrimp until pink and opaque, around 3-4 minutes, then set aside on a plate and cover to keep warm.
In the same preheated skillet, saute the shallots for 2-3 minutes.
Add in the cherry tomatoes, garlic, chicken broth, white wine vinegar, lemon juice, and zest to the skillet and bring the sauce to a simmer, reducing the heat to medium-low.
Allow the sauce to cook for 5 minutes, or the sauce thickens a bit.
Return your cooked shrimp into the sauce, stir to heat through, and garnish with freshly chopped parsley and basil.