Preheat and line pan: Preheat the oven to 350°F and line a 9x13-inch baking pan with parchment paper, leaving an overhang on two sides for easy lifting.
Mix the wet ingredients: In a large bowl, whisk the eggs, vegetable oil, and water together until smooth and slightly foamy.
Add the brownie mix: Fold in the brownie mix and chocolate chips, stirring just until no dry streaks remain; avoid overmixing so the brownies stay fudgy.
Bake the brownies: Pour the batter into the prepared pan and spread it evenly. Bake for 25 to 28 minutes, until the top looks matte and a toothpick comes out with a few moist crumbs.
Cool completely: Let the brownies cool in the pan on a wire rack for a full hour before cutting; this keeps the candy coating from melting in the next step.
Cut into squares: Lift the cooled brownies out using the parchment overhang and cut into 16 even squares on a cutting board.
Melt the candy coating: Place the white candy melts and 1 teaspoon of vegetable oil in a microwave-safe bowl. Microwave in 20-second bursts, stirring between each, until smooth and pourable.
Load the piping bag: Transfer the melted coating to a piping bag or a zip-top bag with a small corner snipped off.
Pipe the bandages: Drag thin, uneven strips of coating across each brownie square, crisscrossing them like bandages and leaving two small gaps near one end for the eyes.
Add the candy eyes: While the coating is still soft, press two mini candy eyes into the gaps on each brownie square.
Let the coating set: Let the brownies sit at room temperature for 10 to 15 minutes, until the candy coating firms up completely before serving or stacking.