Heat oil over medium in a large skillet or braiser pan then add the onion, salt and pepper and cook, stirring occasionally, until just starting to turn translucent, about 4 minutes. Add the diced broccoli stems and cook until bright green, about 1 minute.
Add the orzo and stir until well coated in the aromatics and oil. Pour in the vegetable broth and bring to a simmer. Cook, covered, according to package instructions but add the broccoli florets 5 minutes before the orzo is finished cooking. Be sure to scrape the bottom of the pan frequently to prevent the orzo from sticking.
Remove the pan from the heat and stir in the cream cheese. There should be plenty of residual heat to melt the cream cheese. Then stir in the shredded cheese. Continue to stir until creamy, similar to risotto. Adjust seasoning with more salt and pepper, if desired, and serve garnish with more cheese and parsley, if desired.
