Mix tomato, chile, and oregano in a small bowl. Season with salt; let salsa stand for 30 minutes.

Meanwhile, toss both cheeses with flour in a medium bowl. Cook chorizo in a medium saucepan over medium heat, breaking up with a wooden spoon, until it begins to render, about 1 minute. Add onion and continue cooking until chorizo is cooked and onion is soft and translucent, about 5 minutes.

Transfer chorizo mixture to a small bowl; return saucepan to heat. Add beer; simmer, stirring occasionally and scraping up any browned bits. Whisking constantly, add cheese mixture a 1/4-cupful at a time, allowing it to become blended and smooth between additions. Stir in chorizo mixture. DO AHEAD Queso can be made 30 minutes ahead. Let stand at room temperature .

To reheat, warm skillet with queso fundido over medium heat; stir until melted and bubbly.

Using a slotted spoon, spoon salsa over queso. Serve in skillet or serve in a lava rock bowl like below in the video, with a basket of tortilla chips on the side.