Melt butter in a large saucepan over medium heat. Add onion and 1 tsp. salt and cook until tender and translucent, stirring often, about 5 minutes. Add broth and bring to a boil over high heat, then add peas and cook just until tender, about 4 minutes.
Meanwhile, set aside 1/4 cup tiny mint leaves. Whirl remaining 1/2 cup mint, the oil, and remaining 1/4 tsp. salt in a food processor until mint is very finely chopped.
Purée soup in a blender, working in batches, until very smooth, about 3 minutes per batch.
Ladle soup into bowls, drizzle with mint oil, and sprinkle with almonds and reserved mint leaves.