Prepare the grill to medium-high heat.
Peel and devein shrimp. Cover with plastic wrap and refrigerate until ready to use.
While grill is heating, pulse garlic, jalapeno, ginger, lime juice, orange juice, sugar, vinegar, and turmeric in a food processor until combined. With the motor running, gradually stream in ⅓ cup vegetable oil and process until almost smooth. Season with salt.
Pour half of the sauce into a small bow. Set aside for serving.
Transfer remaining sauce to a medium bowl and add shrimp. Season with kosher salt and toss to coat. (Don't leave the shrimp in the sauce for more than 10 minutes because the acid in the citrus will start to "cook" the shrimp.)
Spray grill with non-stick oil and then immediately arrange shrimp on grill. Grill until bright pink and lightly charred, about 1-1 1/2 minutes per side.
Place grilled shrimp on a platter. Spoon reserved sauce over.
For final touches, season with kosher salt, garnish with sliced jalapeno peppers, lime and/or orange slices and serve with rice if desired.