Melt ghee in a large Dutch oven or stockpot over medium heat. Add pancetta and cook until crisp.
Using a slotted spoon, remove the pancetta from the pot, leaving the fat.
Add onion, celery, and cook, until softened, about 5 to 7 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add peas, chicken stock, and thyme. Stir to combine, bring to a boil, reduce to a slight simmer, and cover. Cook until peas are tender, about 1 hour.
Roughly puree the soup using an immersion blender or a countertop blender. Add half the pancetta and salt and pepper to taste.
To serve, ladle soup into a bowl and top with remaining pancetta.