In a large skillet, heat 1/4 cup oil over medium heat. Add fennel bulb; cook, stirring occasionally, until just tender, about 3 minutes. Add scallions and chopped garlic, and cook for 2 minutes. Add greens, and cook, stirring, until wilted, about 2 to 3 minutes. Remove from heat, and season with fennel seeds and pepper to taste. Stir in mint. Transfer to a bowl until cooled completely. Crumble feta cheese over cooled greens; stir to combine. Taste and adjust seasoning. This should yield 2 cups.
Preheat oven to 375 degrees. Line a baking sheet with a rack. Spray rack with cooking spray. In a small saucepan, melt together remaining 1/2 cup oil and butter over medium heat. Lay one sheet of phyllo on a clean work surface with the long side parallel to edge of counter. Brush liberally with butter-oil mixture. Top with a second sheet of phyllo. Brush second sheet with butter-oil mixture. Cut in half crosswise. Place about 1/4 cup filling at one end of each half. Fold in sides, and roll up to form an egg-roll shape. Brush with butter-oil mixture, and prick in several spots with a toothpick or the tip of a paring knife. Transfer to prepared baking sheet. Repeat with remaining phyllo and filling.
Bake until golden brown and filling is heated through, 20 to 25 minutes. Cool briefly before cutting in half on the diagonal. Serve immediately.
