Soak the peas: Rinse dried peas under cold water and soak them in a bowl of water for a few hours or overnight to soften.
Prepare ingredients: Chop onions, carrots, celery, and any other vegetables. If using meat, dice it into small pieces.
Saute aromatics: In a large pot or Dutch oven, sauté onions, carrots, celery, and garlic in oil or butter until softened.
Add peas and liquid: Drain the soaked peas and add them to the pot. Pour in vegetable or chicken broth (or water), enough to cover the peas by about an inch.
Season and simmer: Add herbs like thyme and bay leaves, along with salt and pepper to taste. Optionally, add diced meat like ham or bacon for flavor. Bring the mixture to a boil, then reduce the heat and simmer uncovered for 1 to 1.5 hours, or until the peas are soft and the soup has thickened.
Blend (optional): Remove bay leaves and thyme sprigs. Use an immersion blender or regular blender to blend the soup until smooth, if desired.
Adjust seasoning: Taste the soup and adjust seasoning if necessary.
Serve: Ladle the soup into bowls and serve hot. Optionally, garnish with toppings like croutons, chopped herbs, or a dollop of sour cream.