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In a medium bowl, whisk together the flour, cinnamon, baking soda and salt.
In stand mixer fitted with the paddle attachment, beat the butter and brown sugar together until light and fluffy. Add the yogurt, and beat until incorporated. Add the eggs, one at a time, beating well after each addition; then add the vanilla. Slowly add the flour mixture, mixing until just incorporated. Add the banana, and beat until well incorporated.
Pour the batter into the prepared loaf pan. Bake until a cake tester inserted in the center of the bread comes out clean, about 1 hour 10 minutes. Remove from the oven and let cool at least 30 minutes before slicing.