Combine 1 cup butter, brown sugar, white sugar, and eggs in a large bowl; mix until smooth.
Mix flour, baking soda, and oats together in another bowl. Add to the butter mixture slowly; mix using an electric mixer until combined.
Spread 3/4 the oat mixture into an ungreased 9x13-inch baking pan using a spatula. Press lightly into the bottom of the pan to make the surface even.
Combine chocolate chips, sweetened condensed milk, 1/3 cup butter, and vanilla extract in a saucepan over medium-low heat. Stir until melted and smooth, about 2 minutes. Pour fudge over the oatmeal base and spread evenly.
Drop tablespoons of remaining oatmeal mixture over the fudge. Press oatmeal down lightly to flatten and swirl into the fudge.
Bake in the preheated oven until the top is lightly browned, 25 to 30 minutes; the chocolate should still be moist. Cool completely on a wire rack, about 45 minutes. Cut into squares.
