Drain and rinse the hearts of palm pasta in a colander. Spread on a clean kitchen towel or paper towels and gently pat thoroughly dry—this is critical to prevent a watery sauce.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Season shrimp with a pinch of salt and pepper, then cook for about 2 minutes per side, until they reach an internal temperature of 145°F (63°C) and are pink and opaque. Transfer to a plate and set aside.
Reduce heat to medium. Add remaining 2 Tbsp oil to the skillet and sauté minced garlic for 30 seconds until fragrant. Pour in coconut cream, lemon zest, and lemon juice (from the zested lemon). Stir and let it bubble gently for 2 minutes until slightly thickened.
Add the baby spinach, a handful at a time, stirring until just wilted, about 1 minute. Season with salt and pepper to taste.
Add the dried hearts of palm pasta to the skillet and gently toss to coat in the sauce. Cook for 2–3 minutes just until heated through—do not overcook, as they can become mushy. Return the shrimp to the pan, toss once, and remove from heat.
Divide among bowls, spoon extra sauce over the top, and sprinkle with dairy-free parmesan and fresh parsley. Serve immediately with the reserved lemon wedges on the side.