Chop the onion and celery. Mince the garlic separately.

Heat the butter and oil in our large two-handled pot over medium heat. Add onion and celery and cook, stirring occasionally, until softened, 4-6 minutes. Add the garlic and dried thyme. Stir until fragrant, about 10 seconds, then stir in the peas. Add water and broth. Bring to a boil over high heat. Reduce heat to maintain a simmer and cool until the peas are tender, about 1 minute.

Puree in batches until smooth. Stir in the milk if desired and season with salt and pepper.