Heat the cooking oil in a pot over medium. Add the garlic and saute for 1-2 minutes. Add the chopped spinach; cook until completely wilted. Then transfer to a colander; drain, pressing to release all excess liquid.
Preheat oven to 400 degrees F. Meanwhile combine sour cream, salt, black pepper and 2/3 cup of shredded cheddar and mozzarella cheese in a medium bowl. Add cooked spinach and chopped asparagus; mix lightly.
Then pour into a shallow baking dish and sprinkle with remaining cheese. Place the baking dish on the middle rack of the oven; bake until cheese is melted and bubbly. Serve with French bread or cracker.