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Melt butter with oil in a large skillet, and add pancetta - cook until beginning to get crisp, 4-5 minutes then remove most of the grease but leave the pancetta.
Using a processor, buzz the carrot, celery & onion until super fine, or finely dice all 3 then add to the pancetta and cook until soft and starting to color a bit, 8–10 minutes, then add the garlic and red pepper flakes, stir for another minute.
Add pork, season with salt and pepper, and cook until fully browned - breaking it up while it cooks.
Pour in the vermouth or wine, scraping across the bottom to get up any stuck on bits, then let simmer on low a couple minutes until reduced by about half.
Stir in the milk or half & half and chicken stock, mix well, add the rosemary and let simmer uncovered about 30 minutes, stirring now and then. You're looking for it to thicken up into a creamy, beautiful sauce.
Boil pasta in salted water, reserve about ½ cup of the starchy water before draining.
Remove the rosemary sprig, then toss the pasta in with the sauce, adding a splash of the pasta water to loosen it a bit if you like, then grate the Parm all over and serve.