With the rack in the middle position, preheat the oven to 190°C (375°F).
Remove the stems from the shiitake mushrooms and slice the caps into thin strips. Set aside.
In a saucepan, bring the broth, garlic and shiitake stems to a boil. Reduce until 60 ml (1/4 cup) of liquid remains. Strain. Add the milk and cream. Set aside.
Season the pork with salt and pepper. In a large skillet over medium-high heat, brown the pork and sage in the butter. Transfer the pork to a baking dish and bake until the pork is cooked but centres are still pink, about 15 minutes.
Cover and let stand for 5 minutes.
Meanwhile, in the same skillet, brown the shiitake caps and white mushrooms in the oil. Season with salt and pepper. Sprinkle with flour and continue cooking for
1 minute. Add the broth mixture and bring to a boil over medium heat, stirring constantly with a wooden spoon. Simmer gently for 2 to 3 minutes. Adjust the seasoning.
Slice the tenderloins and nap with sauce. Serve with Noodles with Butter and Sage.