Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper. Place a metal mixing bowl in the freezer.
To make the cookies, cream together the brown sugar, granulated sugar, and butter. Add the peanut butter, egg, and vanilla, and mix until well combined. In a separate bowl, whisk together the oats, flour, baking soda, baking powder, cinnamon, and salt until well combined. Add this to the sugar mixture and stir until a soft cookie dough forms.
Working in batches, using a heaping teaspoon, form the dough into balls and place on the prepared baking sheets 2 inches apart. Bake, one sheet at a time, for 13 to 15 minutes, or until the edges are set. Cool on the sheet for 5 minutes then transfer to a wire rack to continue cooling (the cookies will harden as they cool). Repeat for the remaining cookie dough. You should have about 36 cookies.
To make the pudding, whisk together the milk, granulated sugar, flour, egg yolks, and salt in a pot. Cook over medium-low heat, continuously stirring, until the mixture starts to bubble and then thicken, 4 to 6 minutes. Turn the heat down to low and stir in the butter and vanilla. Turn off the heat.
To make the whipped cream, take the bowl out of the freezer, add the cream and honey, and then beat until soft peaks form.
Peel and slice the bananas into 1/4-inch rounds. Sprinkle the slices with the lemon juice to prevent them from turning brown.
To assemble, place a layer of cookies and bananas in the bottom of an 8-inch square baking dish. Layer on half of the pudding. Add another layer of cook ies and bananas and then top with the remaining pudding. Spread on top the whipped cream, and then decorate with the remaining cookies and bananas. Chill for at least 4 hours before serving, though if you prefer, you can eat it warm.
Alternatively, you can serve the pudding in six 1/2-pint Mason jars or bowls. Evenly divide the cookies, sliced bananas, and pudding, and then proceed as above.