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Preheat oven to 350 degrees.
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In a large bowl, combine 1 cup flour, baking powder, baking soda, salt, cinnamon, and nutmeg. In a medium bowl, whisk together butter, brown sugar and eggs. Fold into flour mixture. Stir in carrots and walnuts. Spread into bottom of ungreased 8x8 baking dish. Set aside.
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Beat together cream cheese, sour cream, 1/2 cup sugar until smooth. Beat in eggs, one at a time, until smooth. Pour mixture over cake batter in 8x8 baking dish.
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In a small bowl, mix together 1/2 cup Bob's Red Mill 1-to-1 Gluten Free Flour, oats, 1/4 cup brown sugar, cinnamon and butter until it forms a crumbly mixture. Spread over cream cheese layer.
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Bake in preheated oven for 50-55 minutes or until cheesecake is set. Remove from oven and cool for 30 minutes. Transfer to refrigerator and cool completely.