Preheat your oven to 425°F and line a large baking sheet with parchment paper.
Cut the half head of cabbage into 1-inch thick wedges, keeping the core intact so they hold together.
Place the cabbage wedges and drained chickpeas onto the baking sheet. Drizzle with 0.5 tbsp of olive oil and season with half of the sea salt and black pepper.
Roast in the oven for 20-25 minutes, flipping the cabbage halfway through, until the edges are deeply browned and caramelized.
While the vegetables roast, prepare the dressing by whisking together the remaining 0.5 tbsp olive oil, lemon juice, dried oregano, minced garlic, and chopped fresh parsley in a small bowl.
Pat the shrimp dry with a paper towel and season with the remaining salt and pepper.
Heat a non-stick skillet over medium-high heat. Add the shrimp and sear for 2 minutes per side until pink, opaque, and slightly charred.
Arrange the roasted cabbage and chickpeas on a plate, top with the seared shrimp, and drizzle the lemon-herb dressing over everything before serving.