1. Preheat the oven to 400 degrees F. Heat the oil in a large skillet over medium-high heat and cook the garlic, onions and chard stems until softened, about 5 minutes. Stir in the rice and 1/2 teaspoon salt to combine. Add 1 cup water, cover, reduce the heat to low and cook without stirring until the rice is tender but not mushy, about 12 minutes. Uncover, add the spinach, chard leaves and 3/4 teaspoon salt. Cook, stirring, until the greens are wilted, about 3 minutes. Transfer to a large bowl to cool (stirring with a large spoon will speed this up).
2. When the filling is cool, stir in the egg and then the feta, dill, raisins, pine nuts and lemon zest.
3. Place a large piece of parchment paper on a work surface. Lay out one sheet of phyllo and brush all over with some of the melted butter. Lay another sheet crosswise on top and brush with butter again. Working to form a large round of phyllo layers, lay an additional 6 sheets of phyllo dough diagonally over the first 2 sheets, brushing each sheet with butter, so they overlap in the center. Spread the filling in the center of the sheets and bring all the loose ends of the phyllo to rest on top to make a free-form pie, using the butter to help the pieces stick to each other. Lay 4 of the remaining 6 sheets of phyllo evenly over the top of the pie, tucking the edges under the bottom to form an enclosed disk and brushing each piece of dough with butter. Use the last 2 sheets, if necessary, to cover the filling or enclose the circle. Brush the outside of the pie with butter.
4. Lift the parchment with the pie onto a rimmed baking sheet and bake until the phyllo is golden brown and crispy, about 40 minutes. Serve hot or at room temperature with the Tomato Salad on the side.
Toss the tomatoes with the pepperoncini and the olives in a medium bowl. Drizzle with olive oil and season with salt and pepper.