Cook noodles in boiling water & salt in a large pot for 10-12 minutes, stirring occasionally, until tender but firm. Drain. Rinse & drain well.
Chicken Mushroom Filling
Heat olive oil in a large skillet. Add chicken, onion & garlic. Scramble fry for about 7 minutes until onion is softened & chicken is no longer pink.
Add next 4 ingredients. cook, stirring often, until most of the liquid is evaporated. Sprinkle with flour. Stir; add broth & herbs. Heat & stir until boiling & thickened. Transfer to a medium bowl. Let stand for about 15 minutes until cool.
Spread 1/4 cup filling down length of each noodle. Roll up, jelly-roll style. Place rolls in a greased 8-inch pan
Parmesan Cheese Sauce
Preheat oven to 350 F.
Stir milk into flour in a small saucepan until smooth. Heat & stir on medium for about 8 minutes until boiling & thickened. Add cheese, salt & basil paste. Stir. Pour over noodle rolls. Sprinkle shredded, smoked cheddar cheese over all.
Cover with greased foil & bake for 30 minutes. Remove foil & broil, uncovered (if you wish) for 10 minutes until bubbling & golden. Serve.