Preheat oven to 350 degrees (F).
In a microwave-safe bowl, melt the butter with the white chocolate on 70% power for 30 seconds. Stir the mixture and repeat as necessary until mixture is melted. Use caution and avoid overheating. Set aside to cool while you collect the remaining ingredients.
Line an 8" x 8"x baking dish with foil and spritz with non-stick cooking spray. Leave an overhang on the sides so you can easily remove the cooled brownies to cut into squares.
Once the chocolate mixture is lukewarm, stir in the sugar and mix until smooth.
Add the eggs, one at a time, and stir until fully incorporated. Be sure the chocolate mixture isn't hot otherwise the eggs could start to cook.
Stir in the vanilla.
Mix in the flour and salt, stirring until the batter is smooth, then spread into the prepared pan. Batter will be thick.
Bake for 23 - 26 minutes. The top should look set and the sides should be starting to pull away from the sides. A wooden skewer inserted into the center should come out mostly clean. (A few moist crumbs are okay.)
Allow the brownies to cool completely in the pan, then lift them out using the foil and place on a cutting board.
Cut into desired-sized squares.
Place the semi-sweet (or white) chocolate chips and the vegetable oil into a small microwave-safe bowl. Heat on 70% power for 30 seconds then stir. Heat in 10 - 15 second increments until fully melted, but don't overheat.
Drizzle the melted chocolate over the tops of the cut brownies.
Place the brownies in the refrigerator for at least 15 minutes to allow chocolate topping to set before serving.
Store leftover brownies in the refrigerator for up to 4 days.
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