Preheat the oven to 350°F (177°C). Line an 8-inch square baking pan with parchment paper, leaving some overhang on the sides for easy removal.
In a large bowl, whisk the peanut butter and maple syrup until smooth.
Add the milk and vanilla extract and whisk until well combined.
Stir in the rolled oats, cocoa powder, ground flaxseed (if using), baking powder, and salt until the batter is thick and evenly mixed.
Pour the batter into the prepared pan and spread it into an even layer. Sprinkle the chocolate chips over the top if using.
Bake for 25–30 minutes, until the center is set.
Let the oatmeal brownies cool completely in the pan. Use the parchment paper to lift them out, then slice into 9 squares.