If using a ham hock, score it with a knife and sear it in a hot pan on both sides to release some of the fat. Set aside.
Rinse 1 pound of dried peas with water and sort through them to ensure consistency.
In a large stockpot, heat 2 T. of olive oil and sauté 1 cup of chopped yellow onion and 2 cloves of minced garlic. Stir them around on medium heat until the onions and garlic are translucent and fragrant - about 5 minutes.
In the same stock pot, dump in 2 cups diced carrots, 1 1/2 cups diced and peeled red potatoes, your rinsed peas, 1 tsp. salt and 1 tsp. fresh ground pepper. Pour 8 cups of chicken, beef or vegetable stock over all OR add your seared ham hock and 8 cups of water. Stir well and turn the soup on high until it boils.
When the soup boils, turn the heat down low enough to allow a nice, rolling simmer (uncovered) for 45 minutes. Occasionally stir the soup during this time to allow for even cooking. If using a ham hock, skim off any heavy foam that floats to the top. After simmering, the peas will be soft. Add more salt/pepper if needed.