Make Ahead: If wrapped lightly in plastic, the dough can be stored in the refrigerator for several days before baking.
Storage: The cookies will keep in an airtight container for up to one week.
Melt the butter in a medium saucepan over medium heat. Add the bananas and cook, stirring frequently, until they begin to fall apart, darken in color to a light golden-brown, and are very fragrant, 8 to 10 minutes total. Remove the pan from the heat, stir in the cinnamon, and let cool for 30 minutes.
Combine the flour, baking soda, baking powder, and salt in a medium bowl and whisk to combine. Line 3 baking sheets (or as many as you have) with parchment paper or nonstick baking mats.
In the bowl of a stand mixer fitted with the paddle attachment, combine the cooled (but still melted) banana mixture, the vegetable shortening, brown sugar, and ¾ cup (150 grams) of the granulated sugar. (Alternatively, use a hand mixer and large bowl.) Beat on medium speed until fully combined, 1 to 2 minutes. Turn the mixer off and add the eggs and vanilla extract. Mix on medium speed until light and ribbony, 2 to 3 minutes. With the mixer running on low speed, gradually add the dry ingredients, beating until just combined. Stir in the chopped chocolate with a rubber spatula.
Add the remaining ½ cup (100 grams) granulated sugar to a wide bowl. Using a medium 1¾-inch (#40) cookie scoop or 2 tablespoons, portion out the dough and roll into balls. Roll the balls in the sugar and place them 3 inches apart on the baking sheets (about 8 per sheet). Chill in the refrigerator, uncovered, for 30 minutes. (If you can’t fit all 3 sheets in your fridge at once, consolidate the balls on 1 sheet, then divide them again for baking.)
As the dough balls are chilling, preheat the oven to 350°F and set 2 racks at the upper-middle and lower-middle positions.
Bake 2 sheets at the same time, swapping them midway, until the tops are lightly browned, 12 to 14 minutes, then bake the remaining tray on either rack. Let the cookies cool slightly on the baking sheets, then transfer to a wire rack to cool completely, and bake the remaining sheet of dough balls.