Cut onion, onion greens, green garlic, and carrots into large pieces ang place them in a large pot with the thyme, bay leaf, parsley, and peppercorns.
Add enough filtered water to the pot to cover the vegetables by about 3 inches of water.
Place the pot on the stove and heat it over medium-high heat. Bring the water to a boil and immediately turn the heat to medium-low so that the water comes to a simmer. Simmer the stock for about one hour, stirring occasionally. Remove the stock from the heat and allow it to cool to room temperature.
Strain the vegetables from the stock. Pour the remaining stock over a fine mesh strainer into your storage container. Store in the fridge or freezer.