In a large soup pot, add the three tablespoons of butter and melt it over a medium-low heat. Add in the 1/2 cup of onion and of leeks, as well as the 1/4 cups of carrots and celery. Increase heat to medium-high, add in the 1/4 teaspoon of salt and sweat the veggies for about 4 minutes. What is happening here is you are removing the moisture from them, plus breaking down the cell structure, creating more intense flavors for the broth. The salt also helps pull out this moisture. TIP: It is important to salt your food at the beginning of cooking. Salting at the start gives it the opportunity to fully penetrate all components of your dish. Plus, you'll end up using less salt if you do it in the beginning versus the end.
Add in the minced garlic and cook for another minute. Don't let it burn, reducing the heat if you have to.
Toss in the 2 tablespoons of flour and mix well. You want all of the vegetables coated by the flour. Mix until the flour has completely combined with the melted butter. Essentially, this is a roux.
Add the sprig of fresh thyme and the 4 cups of vegetable broth. Increase the heat to medium-high, if it isn't already, and bring the mixture to a boil, all while occasionally whisking the liquid. This will guarantee you have no lumps in your chowder. It will be hella smooth and creamy!
Strain the broth, removing the veggies and thyme sprig. This step is somewhat optional. You can see I left mine in. But these ingredients, a mirepoix if you will, are typically strained.
Transfer the broth back to the stock pot, turn the heat to medium-high, and add in the potatoes. Bring it to a boil and then reduce to a simmer, cooking the potatoes until they are tender. This will take about 5 minutes.
In a separate fry pan, warm 1 tablespoon of olive oil over a medium-low heat. Add in the shredded Brussels sprouts and saute them until they are just tender, about 3 minutes. They will brighten up and turn a gorgeous color green. TIP: Overcooking sprouts makes them smell like rotten eggs due to the high levels of sulforaphane they contain. On the flip side, this chemical fights off cancer.
Using a potato masher, mash up the potatoes in the pot. How much you mash them is a personal choice. I like a lot of potato cubes in my chowder. If you don't, that is okay. It's wrong, but I forgive you. Not really.
Add in the 2 cups of corn and shredded cheddar cheese. Cook for a few more minutes until the cheese has been fully incorporated into the broth.
Transfer the sauteed Brussels sprouts to the soup and remove the pot from the heat. The reason we are cooking the Brussels separately is because if you have ever had over-boiled sprouts, you know how bitter and gross they can be. This method gives you a bit more control. You are welcome to cook them in the chowder, but if you over do it and ruin them... don't bitch at me about it.
We are adding the half and half after to prevent any sort of curdling. With the milk in a measuring cup at least twice its size, add in hot broth one tablespoon at a time. Be sure to whisk the mixture while adding it. Do this until you have equal parts milk and broth in the cup. Now add the mixture back to the soup, slowly, and stirring the soup while doing so.
Garnish with chopped parsley and serve.