Preheat oven to 350°.
To prepare phyllo, line a large baking sheet with parchment paper; coat paper with cooking spray. Place 1 phyllo sheet on paper (cover remaining dough to keep from drying); lightly brush with 1/2 teaspoon oil. Sprinkle with 1 teaspoon powdered sugar. Repeat layers five more times with remaining 5 phyllo sheets, remaining 2 1/2 teaspoons oil, and remaining 5 teaspoons powdered sugar. Cut phyllo stack lengthwise into 3 equal strips; make 5 crosswise cuts to form 18 pieces.
Coat another sheet of parchment paper with cooking spray; cover phyllo stack with paper, coated side down. Place another baking sheet on top of phyllo stack to weigh it down. Bake at 350° for 15 minutes or until golden brown and crisp. Carefully remove top baking sheet and top piece of parchment. Cool phyllo pieces on a wire rack.
To prepare figs, combine port, figs, and cinnamon stick in a saucepan over medium-high heat; bring to a boil. Remove from heat; cover and let stand 10 minutes. Remove figs with a slotted spoon; set aside. Discard cinnamon stick. Bring port to a boil over medium-high heat, and cook until reduced to about 2 tablespoons (about 2 minutes). Remove from heat; stir in reserved figs, 1 tablespoon oil, and salt. Cool to room temperature.
To prepare cream, combine cream cheese, juice, and honey in a small bowl; beat with a mixer at low speed 30 seconds or until smooth. Cover and chill 30 minutes.
Place 1 phyllo piece on each of 6 dessert plates. Top each serving with about 2 teaspoons cream and about 1 tablespoon fig mixture. Repeat the layers once, and top each serving with 1 phyllo piece. Sprinkle evenly with 1 tablespoon powdered sugar. Serve immediately.
Wine note: You'll need some port to prepare this recipe, so make it a bottle you can enjoy right alongside this richly layered and wonderfully textured dessert. A tawny port, like Dow's 10 Years Tawny ($31), provides ample sweetness. And wood aging imparts tawnies with nutty, dried fruit, and treacle flavors that echo those found in the dessert. --Jeffery Lindenmuth