Bring a pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente; reserve 2 tablespoons of pasta water before draining.
Pat the salmon fillet dry with a paper towel and season both sides evenly with half of the sea salt and black pepper.
Heat the olive oil in a non-stick skillet over medium-high heat, then sear the salmon for 4-5 minutes per side until the skin is crisp and the flesh is golden.
Remove the salmon from the pan and set aside; in the same skillet, add the minced garlic and baby spinach, sautéing until the greens are just wilted.
Reduce heat to low and stir in the Greek yogurt, lemon juice, lemon zest, remaining salt, pepper, and the reserved pasta water to create a smooth sauce.
Add the cooked pasta to the skillet, tossing gently to coat every strand in the creamy sauce.
Plate the pasta, top with the seared salmon fillet, and garnish with fresh chopped parsley for a bright finish.