Gather all mise en place, including equipment and ingredients.
Prep all ingredients, according to how it should be diced or chopped per the ingredient list.
In the large, heavy-gauge, wide-bottom pot, heat the oil over medium-high heat.
Sauté all the diced peppers and onions.
Once these vegetables are translucent, add the dried spices (not the thyme or bay leaf yet) and the minced garlic.
Lightly stir until you smell the garlic.
Turn the heat to low.
When the vegetables are fully softened and tender, singer (dust them with the flour) to make a roux, stirring with the wooden spoon.
Deglaze the pan with the white wine, a little at a time, to smooth out the roux.
Gradually add the vegetable stock, whisking to keep it smooth.
Add the chopped fresh thyme and the bay leaf.
Adjust the heat to medium and cook until simmering gently and all the floury taste from the flour is gone.
Once this part tastes good, with no floury feel on your tongue, carefully purée in the blender until completely smooth. (NOTE: Be careful and cover the top of the blender with a towel, as hot things in a blender add pressure - do not overfill and start with a low number, increasing as you can tell it is safe).
Optional - you can strain it to be sure it is smooth, but I don't mind it not strained myself (but my blender does a really good job!)
In a clean pot, bring soup back to a simmering stage over medium heat.
Whisk in grated white cheddar until it is all melted.
Add beer.
NOTE: If not serving right away after making this soup, chill it at this point (after adjusting seasonings, of course. BUT do not add the heavy cream until you are ready to serve it. If you try to reheat the cream, the soup tends to break and taste grainy and not-so-appealing. Or if you reheat very slowly in a double boiler, then it should be fine with the cream already in it.
If serving right away, add the heavy cream. Bring to a simmer.
Adjust seasonings with salt and pepper, as needed.
Serving suggestions: Fat toasted croutons and chives or scallions for garnish.