Pour carrot juice and chicken stock into the measuring cup and heat for 2-3 minutes in the microwave, depending on the strength of your microwave. Set aside.
Add butter and olive oil to a saucepan on medium heat. Melt the butter, then add the dry orzo pasta with salt and pepper to taste. Cook, stirring gently and consistently, for 3-5 minutes (until the orzo turns golden and has a nice toasty, nutty aroma).
Add the carrots to the orzo and stir in for even distribution.
Pour 1 cup of the warmed carrot juice/stock mixture into the orzo. Keep the heat between medium/medium high and stir occasionally, letting the liquid absorb fully into the pasta (about 5-7 minutes). Be careful - if it cooks too fast, you’ll get underdone pasta with burnt sauce bits.
Continue adding liquid 1 cup at a time after the previous batch has mostly absorbed. You’re looking for the consistency of a nice creamy stovetop mac and cheese.
After the last cup has mostly absorbed, remove the pasta from the heat and stir in the parmesan until melted (stir well!).
Add a little dribble of carrot juice or stock if the consistency seems too thick, as the pasta will absorb more liquid as it cools.
Serve immediately! Add a splash of carrot juice when reheating.
Notes
Use vegetable stock and vegan or vegetarian parmesan to adapt for dietary restrictions