Melt butter in a large pot over medium-high heat. Saute onion in hot butter until golden and translucent, about 10 minutes. Stir garlic into onions and saute until fragrant, about 1 minute.
Stir peas and dill into onion mixture and pour in enough chicken broth to cover. Bring to a boil, reduce heat to medium-low, and simmer until hot, 10 to 15 minutes. Stir milk into soup.
Puree soup with an immersion blender or pour pea soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Season with salt and pepper.
