In a large pot or skillet, add olive oil over medium heat. Add carrots and onions and cook for 10 minutes until carrots start to caramelize and brown. Then add garlic and tomato sauce and stir together for a minute. Add stock and Worcestershire sauce and bring to a simmer. Turn heat down to low, cover, and simmer until carrots are tender, probably another 10 minutes.
Blend the sauce either with an immersion blender or slightly cool the sauce and then transfer to a traditional blender and blend until completely smooth.
Cook penne until slightly less than al dente in salted water.
Drain penne, reserving some pasta water. Add carrot sauce to a large skillet and add penne. Pour in 1/2 cup of reserved pasta water and toss together until combined and then penne is tender.
Taste the sauce and adjust seasoning if it needs a pinch of salt.
Serve penne garnished with Parmesan cheese and chives.