Preheat oven to 400 degrees F.
Overlap 3 grape leaves, vein side facing up, to form a solid circle (see Cook's Note*). Place the goat cheese round in the center of the circle. Use 2 roasted pepper strips to wrap around the cheese. Carefully wrap the leaves snugly around the cheese. Repeat with remaining leaves, cheese and pepper strips.
Over high heat, cook the leaf bundles in olive oil for 1 minute on 1 side in an oven-safe skillet. Turn the bundles and cook for 1 minute more. Place the pan in the oven for approximately 3 minutes.
To serve, place vine leaf bundle in the center of a large plate. Open up the leaves and drizzle with olive oil. Serve with crackers or bread.
Preheat oven to 350 degrees F.
Place the red peppers on a baking sheet. Roast in the oven on the top rack for 35 to 40 minutes, turning occasionally, or until the skin is blistered and charred. Immediately transfer the hot peppers to a small bowl and cover tightly with plastic wrap. When the peppers are cool enough to handle, peel off the skin and remove the stem and seeds. Cut into 1-inch wide strips.
Vine leaves should be thoroughly rinsed and dried before using; otherwise, they're too "briny" and brittle. It's important that the leaves completely overlap, with no holes, to prevent leakage of the filling. *Jars of brined vine leaves can be purchased at gourmet stores and at Middle Eastern or Mediterranean specialty stores. (Fresh leaves aren't pliable enough to tightly seal the cheese filling.) **Goat cheese may also be labeled as chevre.