Heat olive oil in a large pot over medium-high heat.
Add diced onion with a large pinch of salt and pepper, cook while stirring frequently for 5 minutes.
Add sliced garlic and dried oregano, cook for 1 more minute.
Stir in vegan basil pesto, crushed tomatoes, and vegetable broth.
Bring mixture to a simmer over high heat.
Reduce heat to medium-low and simmer for 10 minutes, stirring occasionally.
Blend soup carefully with an immersion blender or high-speed blender until smooth and creamy.
Stir in coconut milk and frozen gnocchi.
Bring soup to a simmer over medium-high heat, then reduce heat to medium-low and simmer gently for 5 to 7 minutes until gnocchi is cooked through.
Season with salt and fresh cracked pepper to taste and heat through over medium heat.
Serve garnished with vegan Parmesan cheese, fresh parsley, and red pepper flakes.