Melt butter in a soup pot under medium-high heat. Add chopped onion and cook until softened and translucent, 4-5 minutes.
Add in broccoli stalks and potato to the pot. Stir to coat with butter and add 5 cups of water and 1 tablespoon of Kosher salt. Bring to a boil and then simmer on medium-low. Cover and cook until the stalks and potatoes are tender, about 20 minutes.
Add half of the florets to pot, cover, and cook until bright green, 3-5 minutes. Blend using an immersion blender or can transfer to a blender if you like the soup to be ultra smooth.
Return pot to medium heat and add remaining florets. Cover pot and cook until bright green, another 3-5 minutes. Add 2 cups of cheddar cheese and stir until smooth. Cover and reduce heat to low; set aside while you make your Cheesy Garlic Achaar Toasts.
Place bread slices on a sheet pan. Broil until lightly browned, 2-3 minutes. Turn bread over. Spread each toast with a layer of butter, then spread on Roasted Garlic Achaar. Sprinkle the remaining cheddar on top. Broil until cheese is melty, bubbling and browned in spots, 2-3 minutes.
Remove soup from heat and stir in Greek yogurt. Taste for salt. Add black pepper and crushed pepper flakes if you like.
Cut cheese toasts into strips. Serve soup in bowls with chopped herbs and Cheesy Garlic Achaar Toasts for dipping.