In large shallow Dutch oven, heat oil over medium-high heat; cook chicken, in batches and stirring, until no longer pink inside, about 8 minutes. With slotted spoon, transfer to bowl.
Add mushrooms, garlic and shallots to pan; cook over medium-high heat until liquid is evaporated, about 8 minutes. Stir in flour; cook for 1 minute. Gradually whisk in stock, parsley, oregano, thyme, sage, salt and pepper; bring to boil. Reduce heat and simmer, stirring occasionally, until thickened, about 5 minutes. Return chicken to pan.
Meanwhile, in small saucepan, boil wine until reduced to 1/2 cup; stir into chicken mixture. Let cool completely.
Lay 1 sheet of phyllo on work surface; brush with butter. Top with second sheet; brush with butter. Mound 1 cup filling 2 inches from 1 short side. Fold sides over; roll up. Place, seam side down, on parchment paper–lined baking sheet. Brush with butter. Repeat to make 8 bundles. Bake in 425°F oven until golden, about 15 minutes. Let cool slightly.