Heat olive oil in a large pot over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.

Stir in the minced garlic and cook for another minute until fragrant.

Add diced potatoes and chicken broth; bring to a boil. Reduce heat and let simmer until potatoes are tender, about 15 minutes.

Pour in heavy cream and bring to a gentle simmer. Stir in the shredded cheese until melted and smooth.

Add diced ham, thyme, salt, and pepper. Stir well and let simmer for an additional 5 minutes.

Remove from heat and let cool for about 10 minutes before serving. Garnish with additional cheese if desired.