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Preheat oven to 350 degrees F. Grease bottom and sides of 9x13-inch baking pan with coconut oil.
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In large bowl, toss chopped nuts with cinnamon until well combined.
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In medium bowl, stir together nut butters and sunflower seed butter. Set aside.
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Unroll phyllo dough sheets and cut stack in half. Cover phyllo with dampened cloth to prevent drying during prep.
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Arrange two sheets of dough in baking pan, sprinkle three tablespoons of nut mixture on top, drizzle nut butter mixture over each layer, then brush on small amount of coconut oil. Repeat until remaining ingredients are used.
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With sharp knife, slice baklava into diamond shapes.
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Bake for about 50 minutes until golden and crisp.
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While baklava is baking, combine honey, water and vanilla in saucepan. Bring mixture to a boil; reduce heat and simmer for about 20 minutes.
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Remove baklava from oven and immediately spoon syrup evenly over dessert. Let cool before serving. Store in refrigerator.