Position racks in the upper and lower thirds of the oven and preheat to 325 degrees F. Line 2 baking sheets with parchment.
Combine the peanut butter, butter, brown sugar, salt, baking powder, baking soda and vanilla extract in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium speed until smooth and fluffy, about 2 minutes. Scrape the bowl and paddle with a rubber spatula.
Add the egg and water, mix on low speed then increase the speed to medium, until smooth and combined.
With the mixer running on low speed, add the flour and mix until just combined then add the oats and mix until just combined. Scrape the bowl and paddle with a rubber spatula.
Reserve 2 to 3 tablespoons of the candy-coated chocolates and peanut butter cups for topping and add the rest to the cookie dough, along with the toffee bits and chocolate chips. Mix on low speed until combined.
Scoop six 1/4-cup mounds of dough onto each of the prepared baking sheets. Flatten each mound to about 3/4 inch thick and arrange the reserved candy-coated chocolates and peanut butter cups on top of the cookies.
Bake until puffed and slightly golden around the edges, 18 to 20 minutes, rotating and switching the positions of the baking sheets after 10 minutes. Let cool completely on the baking sheets.