Heat a medium pot. Add coconut oil, onion and garlic. Cook until onions are tender, about 5 minutes.
Add the broth, asparagus, and peas and bring to a boil. Reduce heat and cook 5 minutes.
Transfer 1/3 of the the mixture to a blender. Carefully blend until smooth and return to pot. Alternatively, use an immersion blender to blend some of the soup, leaving some chunkiness.
Continue cooking for about 3 minutes until asparagus and peas are tender but still bright green. Remove from heat and stir in tarragon, dulse, salt, and pepper. Garnish with chives before serving.