Heat olive oil in a large skillet over medium heat and add peeled garlic cloves.
Cook garlic, stirring often, until deep golden brown on all sides.
Remove garlic with a slotted spoon and place in a blender; reserve the oil in the pan.
Add cilantro, lemon juice, salt, pepper, oregano, and a drizzle of olive oil to the blender.
Blend until completely smooth and creamy; set sauce aside.
Return skillet to medium-high heat and add shrimp in a single layer.
Sear shrimp 2 minutes per side until just opaque halfway through.
Pour the green sauce over the shrimp and stir gently until heated through, 1–2 minutes.
Serve immediately over white rice with extra sauce on top.