Place the shrimp in a resealable bag or medium bowl.
Make the marinade: In a small bowl or liquid measuring cup, mix together the garlic, ginger, olive oil, honey, and soy sauce.
Pour half of the marinade on the shrimp, massaging through the bag or stirring to coat. Reserve the remaining marinade. Marinate the shrimp in the refrigerator for 15 minutes.
In a medium pan, heat the olive oil over medium heat. Remove the shrimp from the marinade, discarding the marinade, then add to the pan and cook for about 1 minute, then flip. Pour in the reserved marinade and continue cooking until the shrimp are opaque and just firm, about 1 minute more. Remove the shrimp from the pan and continue cooking the marinade until reduced and thickened, about 5 minutes.
Serve the shrimp over cooked rice with steamed broccoli alongside. Pour the reduced sauce over the shrimp and garnish with scallions.