Step 1Heat the oven to 425 degrees. Cut 4 sheets of baking parchment into 15- by 12-inch pieces. Fold each piece in half and cut into the shape of half a heart. Open to reveal a whole heart and brush each sheet lightly with olive oil along the fold in the middle. Set aside.
Step 2Combine the corn kernels, mushrooms, garlic, thyme, wine and cream in large bowl and toss to mix well. Season with salt and pepper to taste.
Step 3Divide the mixture among the parchment sheets, mounding along the fold on one side of the heart. Fold the parchment over and tightly crimp the edges to seal completely. Transfer to a baking sheet.
Step 4Bake 30 minutes. Transfer to serving plates and slit open just before serving. Serve immediately.