Mince the vegetables very small or chop in a food processor.

In a heavy bottom Dutch oven, melt the butter over medium-low heat.  Add the vegetables and saute, stirring often for 15 minutes until the vegetables begin to carmelize.

Sprinkle the flour over the vegetables.  Mix completely and cook, stirring constantly, for another 5 minutes.  Deglaze the pot with the wine. Whisk into the flour mixture vigorously and allow to cook for a minute.

Pour in the chicken broth.  Whisk vigorously to incorporate all of the flour into the broth.  Allow the soup to simmer for 10 minutes.

Add the milk and both the Velveeta and cream cheese.  Reduce the heat to low.

Cook, stirring often until the cheese melts and the soup begins to thicken a little bit.  This could take up to 20 minutes. Don’t rush this process. If the heat is too high, the soup will scorch.

Season with salt, pepper, and hot sauce.  Stir well.

If the soup isn’t hot enough for your personal eating preference, warm it in a double boiler or by the cup or bowl in the microwave.  Don’t let the soup boil. It will curdle and not look appetizing at all. Using the microwave at half power to heat the soup is perfection!

Enjoy.