Drop about 14 heaping teaspoonfuls of Nutella onto a nonstick baking sheet (or one lined with waxed paper). Place in the freezer until totally frozen.
Whisk together flours, salt and baking soda in a medium bowl.
In a large bowl, beat butter and sugars with an electric mixer; mix on medium speed until pale and fluffy. Reduce speed to low and add egg and vanilla; mix until combined. Mix in the banana. Add the flour mixture; mix just until combined. Stir in the oats. Refrigerate the dough for at least a couple of hours, until fairly firm.
Preheat the oven to 375 degrees F. Line baking sheets with parchment paper, silpat mats, or spray with nonstick spray.
Drop dough by tablespoonful onto the prepared baking sheets (or use a small cookie scoop), spacing about 3 inches apart. Place a frozen piece of Nutella on top of the cookie dough, then drop another tablespoonful of cookie dough on top of the Nutella. Use your fingers to surround the Nutella with the cookie dough. Sprinkle a few mini chips on top.
Bake cookies until golden brown and just set, 14 to 16 minutes. Let cool on sheets on wire racks 5 minutes. Transfer cookies to wire racks; let cool completely.
Notes
Be sure to use a banana that is well on its way to the trash can. The darker it is, the softer and sweeter it becomes.
Cookies can be stored in airtight containers at room temperature up to 2 days. They also freeze well.