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Preheat oven to 375 degrees F. Grease or line muffin tin with muffin cups.
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In a large bowl, stir together all-purpose flour, whole wheat flour, sugar, baking soda and salt. Set aside.
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In a separate bowl, whisk together eggs, butter, Greek yogurt, milk, lime juice, lime zest, vanilla extract and chia seeds, if using.
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Slowly whisk dry ingredients, a little at a time, into wet ingredients, reserving 1-2 tablespoons of the flour mixture to toss with the blackberries. Continue adding the flour mixture, whisking just until combined.
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Add blackberries to remaining 1-2 tablespoons of flour in bowl, and toss to combine. Gently fold flour coated blackberries into the batter. Using an ice cream scoop or ¼ cup measuring cup, scoop muffin batter into lined muffin tin.
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In a small bowl, stir together granulated sugar, lime zest and chia seeds, if using, to form lime sugar topping. Sprinkle muffin batter with sugar topping and bake in preheated 375 degree F oven for 12-15 minutes, or until a wooden toothpick inserted in the center comes out clean.
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Let muffins cool in pan for 5-10 minutes before transferring to a wire rack to cool completely. Muffins can be stored in a plastic storage container for 2-3 days or frozen in freezer safe packaging for up to 6 months.