Step 1In a large saucepan, heat the olive oil and saute the green onions until the whites are translucent and the greens are wilted, 2 to 3 minutes.
Step 2Add the arugula and 1 cup broth. Cook, covered, until the leaves wilt, about 3 minutes. Remove and cool.
Step 3In a blender, puree the arugula mixture in batches until very smooth.
Step 4Return the puree to the saucepan and add the remaining 2 cups broth. Bring the soup back to a simmer, but do not boil.
Step 5Season with one-quarter teaspoon salt and pepper to taste.
Step 6To serve, ladle the soup into four bowls, adding the cream to each bowl in a pattern, but not stirring to combine. Divide the arugula blossoms among the bowls, spooning onto the center of each. Serve immediately.