Preheat the oven to 350°F. Line an 8-inch square metal pan with aluminum foil, then coat the foil with nonstick cooking spray.
In a large metal bowl set over saucepan of simmering water, melt the chocolate with the coconut oil, stirring with a rubber spatula, until smooth. Remove from heat.
In a mixing bowl, whisk together the milk, vanilla, and cornstarch. Add the warm chocolate mixture to the mixing bowl and stir until well combined. Add the sugar and mix well.
Sift in the flour, cocoa, baking powder, and salt and fold until well combined (a few lumps are okay). Pour the batter into the prepared pan and spread it to the edges.
Drop spoonfuls of the peanut butter mixture onto the brownie batter in the pan, then use a butter knife to swirl it in. Bake until a toothpick inserted in the center comes out mostly clean, 18 to 20 minutes.
When cool enough to handle, lift the foil out of the pan, slice the brownies, and serve!