Pat the raw shrimp completely dry with paper towels and season with sea salt, black pepper, and dried oregano.
Slice the halloumi cheese into 1/4-inch thick rectangles and pat the surfaces dry to ensure a crisp sear.
Heat a large non-stick skillet over medium-high heat and add 0.5 tsp of extra virgin olive oil.
Place the halloumi slices in the pan and sear for 1-2 minutes per side until a deep golden-brown crust forms, then remove and set aside.
Add the remaining 0.5 tsp of olive oil to the same pan along with the minced garlic, sautéing for 30 seconds until fragrant.
Add the shrimp to the skillet in a single layer and cook for 2-3 minutes per side until they are pink, opaque, and slightly curled.
In a small bowl, whisk together the fresh lemon juice and lemon zest.
Place the fresh arugula in a large bowl and toss with half of the lemon mixture.
Divide the dressed arugula between plates and top with the warm seared shrimp and crispy halloumi slices.
Drizzle the remaining lemon mixture over the top and serve immediately.