Peel and cube Yukon Gold potatoes into uniform half-inch pieces. Rinse under cold water to remove excess starch and prevent a gummy texture. Set aside.

Melt butter in a large pot or Dutch oven over medium heat. Add chopped onion and cook for 5 to 7 minutes, stirring occasionally, until softened and translucent.

Add minced garlic and stir constantly for 1 to 2 minutes until fragrant. Do not let the garlic brown or it will turn bitter.

Sprinkle flour over the onion and garlic. Stir and cook for 1 to 2 minutes until the flour smells slightly nutty and loses its raw smell. This creates the roux that thickens the soup.

Gradually whisk in broth a small splash at a time, scraping the bottom of the pot as you go. Whisk until smooth and lump-free, then bring to a gentle simmer.

Add rinsed potato cubes and stir well. Cover and cook on medium-low for 15 to 20 minutes, stirring every 5 minutes, until potatoes are completely tender and fall apart easily when pressed.

Use an immersion blender to pulse the soup several times, blending about half to two-thirds while leaving visible potato chunks for texture. If using a standard blender, carefully ladle out half the soup, blend smooth, then return it to the pot.

Reduce heat to low. Slowly stir in milk and heavy cream, then add parsley, chives, and thyme. Heat gently for 5 minutes, stirring often. Do not let the soup boil after adding the dairy.

Remove pot from heat completely. Add shredded cheddar in small handfuls, stirring after each addition until fully melted before adding more. Adding cheese off the heat prevents a grainy texture.

Taste and season with salt, pepper, and optional smoked paprika or cayenne. Ladle into bowls and garnish with crumbled bacon, extra cheddar, sour cream, or fresh chives.