Jalapeñoseeds and membranes removed and finely minced
up to 1/2 cup fresh chopped cilantroto taste
In a medium pot, melt 1/2 tablespoon butter over low heat. Add minced garlic and jalapeño and saute for a minute or until starting to soften and garlic is starting to turn golden. Add tomatoes to pot and cook a minute or two more. Remove garlic/jalapeño/tomato mixture with a spoon and set aside.
Add remaining 2 tablespoons butter to the pot and melt. Whisk in flour and stir continuously for a couple of minutes as roux bubbles and turns golden brown. Gradually whisk in cream, pausing between additions to make sure that lumps are smoothing out. While continuously stirring, bring mixture to a low simmer and cook for about 5 minutes or until thickened.
Remove pot from heat. Add 1/2 cup grated cheese to cream mixture and stir until completely melted. Repeat with the remaining cheese, adding 1/2 cup at a time and making sure it is totally melted before adding the next 1/2 cup. Add salt, garlic/jalapeño/tomato mixture, and sour cream. Stir until well incorporated. Taste and add additional salt, if desired.
Transfer queso to a serving bowl and top with as much cilantro and avocado as you prefer. You may stir it in or leave it on top as a garnish (I stir some in and pile the rest on top, plus a few extra diced tomatoes for color).
With seeds and membranes removed, one jalapeño should not be spicy at all. If you like spicier queso, add additional jalapenos or leave the seeds and membranes intact before dicing. You can also decrease/increase the garlic to your taste, toss in some diced green chiles, add more cilantro or leave it out altogether...it's up to you!
If you don't cook your roux long enough, you may be able to taste the flour in the final queso.
If your pan is too hot or still over the burner when you add the cheese, the cheese may end up clumping. Similarly, if you try to add too much cheese all at once, it will probably end up separating and clumping. Add no more than 1/2 cup at a time and stir until it is completely melted before adding the next half cup.