Lightly coat a 5-quart slow-cooker insert with cooking spray. Line the bottom with parchment paper and lightly coat with spray.
In a large bowl, use a whisk to combine eggs, cocoa, salt, baking powder, espresso powder and vanilla, and mix until smooth.
Place the butter in a small saucepan to melt. Once melted, add the sugar and stir until the sugar has dissolved. Pour sugar mixture into cocoa mixture and whisk until well combined. Add the flour and chocolate chips, using a silicone spatula to mix until smooth.
Transfer the batter into the prepared slow cooker and smooth the top. Cover and cook on low, 3-½ hours. Uncover and cook for 30 minutes. Remove the insert from the slow cooker and run a knife around the edge to loosen the brownie cake. Turn out onto a wire rack and cool for about 2 hours. Cut and serve.