Preheat the oven to 350°F (175°C) and grease a 9×13-inch baking dish.
In a large bowl, stir together the white cake mix, the 2 large eggs, and the 1/3 cup vegetable oil until well combined; the batter will be thick.
Transfer about 2/3 of the batter to the prepared baking dish and press it evenly to completely cover the bottom.
In a microwave-safe bowl, combine the 14-ounce can of sweetened condensed milk, the heaping cup of semisweet chocolate chips, and the 1/4 cup cubed salted butter. Microwave for 30 seconds, stir; microwave an additional 20 seconds, stir; if the chocolate chips and butter are not fully melted, microwave another 20 seconds and stir until the mixture is smooth.
Pour the chocolate-condensed milk mixture evenly over the pressed batter in the baking dish.
Drop the remaining batter by small spoonfuls over the chocolate layer (it’s fine if there are gaps).
Bake for 20 to 24 minutes, until the edges are set and a toothpick inserted into a cake portion comes out mostly clean.
Let the pan cool until the bars are firm, then cut into squares.