Heat ½ cup oil in a pot over medium-high heat. Add scallions and garlic; cook until soft, 3-4 minutes. Add chard and herbs; cook, stirring, until tender, 12-15 minutes. Season with salt and pepper; cool. Stir in feta.
Grease a 13 x 9-inch baking sheet. Gently layer the baking shee with half of your phyllo dough, brushing each layer with olive oil and allowing the ends to hang off the edge. Spread the chard mixture over the phyllo dough.
Top with remaining phyllo, again carefully brushing each layer with olive oil. Fold phyllo hanging over edges onto top of pie; brush with 1 tbsp. oil.
Bake 20 minutes. Reduce heat to 350°; bake until golden brown, 18-20 minutes. Let cool slightly.