Preheat the oven to 350 degrees F and line a 8-inch square pan with parchment paper, leaving some overhang for easy removal later. Set aside.
In a medium-sized bowl, stir together the flour, rolled oats, brown sugar and salt. Add the melted butter and stir until the mixture resembles moist crumbs.
Press the crumbs into the prepared pan and press firmly and evenly. Bake for 11-13 minutes until the edges turn slightly golden brown. Remove from oven and let cool while you prepare the filling.
To the bowl of a stand mixer with the paddle attachment (or using an electric hand mixer), add the peanut butter and softened vegan butter. Mix until combined, or for about 1 minute. Add the powdered sugar and mix until combined, scraping the sides as needed.
Spread the peanut butter mixture evenly onto the crust and place in the refrigerator to chill while you prepare the chocolate topping.
In a microwave-safe bowl, melt the chocolate chips and oil in 30-second increments, stirring in between, until melted and smooth.
Spread the chocolate over the peanut butter layer, sprinkle with coarse salt (optional), and return to the refrigerator to chill for at least 30 minutes.
Cut into squares, serve and enjoy!