Reduce the heat to medium and melt the butter in the same pot. Use a wooden spoon to scrape off the flavorful fond at the bottom.
Add the onions, carrots, and chopped celery and cook for 5 minutes, stirring occasionally.
Combine the seasonings, then add them to the pot together with the garlic, Worcestershire sauce, and hot sauce.
After a minute, add the flour and stir to coat all the vegetables. Cook for 2 minutes, stirring continuously.
Slowly add the broth. Scrape the bottom of the pot as you stir.
Add the half and half in small splashes. Next, add the peas to the soup and bring everything to a gentle boil.
Simmer the soup uncovered.