Preheat the broiler to 500°F. Bring the butter to room temperature to soften.
Trim the roots from the green onions and remove the tops. Place the bottoms in a pan with a little olive oil and salt, and then broil them until the onions are charred on all sides, a few minutes to each. Remove from the oven and then let the onions cool completely.
Place all the ingredients in a food processor and pulse until all ingredients are well incorporated. Check the seasoning to your taste and adjust as necessary.