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Preheat the oven to 350 F/ 170 C.
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In a large, deep skillet or wide pot, sauté the onions in olive oil until soft and translucent. Add the scallions until soft, about 2 minutes. Add spinach and chard and sauté until wilted, about 5 minutes. Turn off the heat. Add dill and parsley and mix well.
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Put the mixture in a large bowl. Crumble tofu into very small pieces, add to the mixing bowl and mix well.
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Brush the bottom of a 9x13-inch baking pan with olive oil. Arrange a sheet of phyllo pastry in the bottom of the pan and brush it with olive oil. Arrange a second sheet of phyllo on top of the first, gently working out any bubbles between the two. Brush this layer with olive oil, as well. Repeat until you've layered 12 sheets, finishing with a phyllo sheet.
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Evenly spread the spinach mixture over the surface of the phyllo, smoothing out the top with the back of a spoon or a spatula. Arrange 8 more phyllo sheets on top of the spinach filling, in the same manner, brushing them with olive oil. Brush the top sheet with olive oil and sprinkle with sesame or Nigella seeds.
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Bake for about 45 minutes, until the pastry is golden brown and crispy. Let it cool completely before cutting through and serving.