Heat vegetable oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the diced onion and sauté for 5 minutes until soft and translucent.
Stir in the minced garlic, cumin, chili powder, salt, and cayenne; cook for 1 minute until fragrant.
In a medium bowl, whisk together the masa harina and warm water until a smooth slurry forms with no lumps.
Pour the masa slurry into the pot and stir constantly for 2-3 minutes as the mixture thickens into a paste.
Gradually whisk in the chicken broth and red enchilada sauce until well combined, then bring to a gentle boil.
Reduce the heat to low and stir in the cubed Velveeta and shredded cheddar cheese until completely melted and smooth.
Add the shredded chicken, black beans, diced tomatoes with green chiles, and frozen corn to the pot.
Simmer the soup for 15-20 minutes, stirring occasionally to ensure the bottom does not scorch.
Serve hot with optional garnishes such as crispy tortilla strips, diced avocado, and fresh cilantro.