Melt butter in a medium saucepan over medium heat. Once it foams, add the shallot and garlic, and saute until softened, about 3 minutes.
Add the flour and cook while stirring until it becomes a light blonde color.
Slowly stir in the heavy cream, and the drained spinach, and simmer until it starts to thicken, about 5 minutes.
Stir in the artichoke hearts, tomatoes, and cheese and cook until the cheese is melted. Remove to a serving bowl and serve with tortilla chips.