In a large mixing bowl, whisk the flour with the 2/3 cups sugar and salt. In a separate large mixing bowl, combine the warm milk with the yeast and 2 tablespoons sugar. Let it sit and get foamy.
Mix the banana in with the milk mixture. Add the dry ingredients in batches, mixing well, until all ingredients are incorporated. Add the softened coconut oil. Turn out onto a floured surface and knead for a good 10 minutes until smooth and elastic.
Clean the mixing bowl, and lightly grease it with some canola oil. Add the ball of dough, spinning it into the bowl to get it lightly coated in oil. Cover with plastic wrap or a towel, and set aside in a warm place to rise for about an hour and a half. It should double in size.
Line a large baking sheet with parchment paper and lightly coat parchment with oil. Divide the dough in two, and form into two rough squares on the parchment. Let rise in the refrigerator for about 30 minutes.