Melt butter with oil in a Dutch oven over medium heat. Add onions, celery, carrot and garlic; sauté until softened, about 5 minutes.
Add potatoes and broth; stir to combine. Bring to a boil.
Reduce heat and simmer, uncovered, stirring occasionally, for 30 minutes.
Stir in 1 cup cheese, milk, salt, pepper and turmeric; cook, stirring, for 4 minutes. Remove from heat.
Using a hand blender, purée mixture until smooth.
Serve topped with toppings.