In a medium saucepan or pot, bring the shallot, half the cauliflower florets, milk, and ½ teaspoon salt to a simmer. Cook over medium-low heat, covered, until the cauliflower is tender, about 20 minutes.

Puree the cauliflower mixture with an immersion blender, or transfer to a food processor or stand blender, until smooth.

Return to the pot and stir in the cheese. Cook stirring constantly until melted.

Add some extra milk or water, if necessary, so the cauliflower queso is a drizzle-able consistency.