Melt butter in a large skillet over medium-high heat. Add 1 Tbsp. oil to pan; swirl to coat. Add shallots to pan; sauté 3 minutes. Add cremini and exotic mushrooms, 1/2 tsp. salt, and 1/4 tsp. pepper; sauté 6 minutes or until mushrooms are browned. Add thyme and 3 garlic cloves; sauté 1 minute. Stir in wine; bring to a boil. Cook 1 minute or until liquid almost evaporates, scraping pan to loosen browned bits. Remove from heat; stir in cream cheese and 1 Tbsp. chives. Add reserved porcini mushrooms.

Heat a saucepan over medium-high heat. Add remaining 1 Tbsp. oil to pan; swirl to coat. Add remaining 3 garlic cloves to pan; sauté 30 seconds. Add the reserved porcini liquid, 2 3/4 cups milk, remaining 1/2 tsp. salt, and remaining 1/4 tsp. pepper; bring to a boil. Combine remaining 1/4 cup milk and flour in a small bowl; stir with a whisk. Add flour mixture to milk mixture, and simmer 2 minutes or until slightly thick, stirring constantly with a whisk.

Spoon 1/2 cup sauce into an 11 x 7-inch glass or ceramic baking dish coated with cooking spray, and top with 3 noodles. Spread half of mushroom mixture over noodles. Repeat layers, ending with remaining sauce. Sprinkle cheese over top. Bake at 350°F for 45 minutes or until golden. Top with remaining 1 Tbsp. chopped chives.