- 9 (17- by 12-inch) phyllo sheets, thawed if frozen
- 3/4 stick (6 tablespoons) unsalted butter, melted
- 2/3 cup rinsed and drained bottled red peppers (7-ounce jar), finely chopped and patted dry
- 5 ounces soft mild goat cheese (2/3 cup)
- 1/2 cup olive oil
- 1 tablespoon balsamic vinegar
- 1 teaspoon Dijon mustard
- 1/4 teaspoon salt
- 3 tablespoons extra-virgin olive oil
- 8 ounces frisée, torn into bite-size pieces (8 cups)
- 2 tablespoons chopped pitted Kalamata or other brine-cured black olives
- Cover phyllo stack with 2 overlapping sheets of plastic wrap and then a damp clean kitchen towel. Arrange 1 phyllo sheet on a work surface with a long side nearest you (keep remaining sheets covered) and brush with some butter. Top with 2 more phyllo sheets, brushing each with butter.
- Cut buttered phyllo stack crosswise into 5 (12- by 3 1/3-inch) strips.
- Put 2 teaspoons red peppers and 2 teaspoons goat cheese near 1 corner of a strip and fold corner of phyllo over to enclose filling and form a triangle. Continue folding strip (like a flag), maintaining triangular shape. Put triangle, seam side down, on a baking sheet and cover with plastic wrap. Make 14 more triangles in same manner, using remaining phyllo and filling (you may have a little butter left over).
- Heat oil in a 12-inch nonstick skillet over moderately high heat until hot but not smoking, then fry triangles in 2 batches until golden, about 1 minute per side. Transfer with tongs to paper towels to drain.
- Whisk together vinegar, mustard, and salt in a large bowl, then add oil in a slow stream, whisking until emulsified. Add frisée and olives and toss with dressing, then season with pepper. Mound salad on plates and arrange phyllo triangles alongside.