Heat half of the butter in a large pot over medium heat. Add diced onion and cook until translucent, about 2-3 minutes.
Add minced garlic, Italian seasoning, dried parsley, and dried oregano; cook until fragrant, about 1 minute.
Add diced potatoes and cooked bacon bits to the pot. Pour in enough chicken broth to cover the potatoes. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 15-20 minutes.
In a separate saucepan, melt the remaining butter over medium heat. Whisk in flour to create a roux. Gradually add heavy cream, stirring continuously until the mixture thickens. Add this mixture to the pot with potatoes.
Mash some of the potatoes in the pot for a thicker texture. Stir in cream cheese until melted and incorporated, and add a bit more broth if the soup needs to be thinned out.
Season with salt and black pepper. Garnish with chives and shredded cheddar cheese before serving.