In a large pot, combine the chopped cauliflower, carrots, celery, and onion. Pour in enough chicken or vegetable stock to cover the vegetables completely. Bring the mixture to a boil over medium-high heat, then reduce to a simmer. Cook for about 15 minutes, or until the vegetables are tender and easily pierced with a fork.

While the vegetables are cooking, melt 4 tablespoons of butter in a separate saucepan over medium heat. Whisk in 1/4 cup of all-purpose flour and cook for 2 minutes until lightly golden. Gradually add 4 cups of milk while whisking continuously to avoid lumps, cooking until the mixture thickens—about 5 minutes. The cheese sauce should become smooth and creamy.

Once the vegetable mixture is tender, remove the pot from heat and stir in 2 cups of shredded Mexican blend cheese. Add the prepared cheese sauce, along with two bay leaves, 1 teaspoon of dried basil, and salt and pepper to taste. Return the pot to low heat and let everything simmer together for about 10 minutes, stirring occasionally.

After simmering, remove the bay leaves and carefully use an immersion blender to purée the soup until it's smooth and velvety. If you prefer a chunkier texture, reserve a few vegetable pieces before blending and stir them back in after blending.

Taste the soup and adjust the seasoning with more salt or pepper, if needed. Serve the creamy and cheesy cauliflower soup hot, garnished with fresh herbs or a drizzle of olive oil. Pair with crusty bread for a cozy meal.