Melt the unsalted butter in a Dutch oven over medium heat. Add the yellow onion and cook for 4 to 5 minutes, stirring, until soft and translucent. Stir in the garlic and cook for 30 seconds.

Sprinkle the all-purpose flour over the onion and stir for 1 minute. Whisk in the low-sodium vegetable broth a little at a time until smooth, scraping the bottom of the pot.

Add the russet potatoes, kosher salt, and black pepper. Bring to a gentle simmer, cover, and cook for 16 to 20 minutes, stirring once or twice, until a fork slides easily into the potato cubes.

Remove the pot from the heat. Use a potato masher to gently mash the potatoes in several places, about 8 to 10 presses total, leaving plenty of chunks.

Stir in the room-temperature whole milk. Return the pot to low heat and warm gently for 3 to 4 minutes without boiling. Turn off the heat, then stir in the freshly grated sharp cheddar cheese and sour cream until creamy.

Let the soup stand for 5 minutes so it can thicken slightly. Taste and adjust the seasoning. Ladle into bowls and top with fresh chives and optional sharp cheddar cheese.