Heat olive oil in a large pot over medium low heat. Add sliced onions and cook slowly, stirring occasionally, until deeply caramelized and golden brown, about 20 to 30 minutes.
Remove onions temporarily. Season chicken with salt and pepper, then sear in the same pot until lightly golden on both sides.
Return onions to the pot. Add garlic and thyme. Stir for one minute until fragrant.
Pour in broth and stir in dry orzo. Bring to a gentle simmer.
Cover and cook until orzo is tender and liquid is mostly absorbed, about 10 to 12 minutes. Stir occasionally.
Stir in shredded cheese until melted and creamy. Add optional cream if desired. Adjust seasoning and serve warm.
