Combine the 1 1/2 cups flour, 1 1/2 teaspoons nutmeg, 1/2 teaspoon baking soda, 1 teaspoon baking powder and 1/2 teaspoon salt in a medium bowl. Whisk to break up any lumps.
Place 1 cup brown sugar, 1/4 cup granulated sugar and 1 cup vegan butter in the bowl of a stand mixer fitted with the paddle attachment. Beat at medium speed until light and fluffy, about 3 minutes.
Add the 2 eggs, one at a time, letting the first one beat in completely before adding the next. Add the 2 teaspoons vanilla, and 1 medium banana and mix on low until combined. Scrape down the sides of the bowl with a rubber spatula.
Add the flour mixture into dough then beat on low to incorporate. Finally, add the 2 cups oats, 1 cup chocolate chips, and 1 cup nuts and mix on low until evenly combined.
Cover mixing bowl and refrigerate dough for 30 minutes. Meanwhile, heat oven to 350°F and line 2 baking sheets with parchment paper.
Scoop cookie dough into balls with a medium cookie scoop and place on the prepared baking sheets about 1-inch apart. Press down lightly to encourage spreading. Bake until golden on the bottom, about 10 to 12 minutes. Cookies will not be completely set in the middle. They will continue to set up as they cool.
Let cool for 10 minutes on the baking sheet then remove to a wire rack to cool completely.