Preparation of Equipment and Ingredients: Begin by preheating your oven to 350°F (177°C). Line a 9x13 inch baking pan with parchment paper, or coat it generously with non-stick cooking spray. This ensures easy removal and cutting of the bars once baked and cooled.
Preparing the Crust and Crumble: In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Cream these ingredients together until light and fluffy. Sequentially incorporate the baking soda and salt. Gradually add the all-purpose flour and quick-cooking oats to the mixture, stirring until the mixture is well combined and crumbly in texture. Press half of this oat mixture into the bottom of your prepared pan, forming a firm, even layer. Place this in the preheated oven and bake for 13 minutes, until just set and slightly golden.
Making the Cream Cheese Filling: While the base is baking, prepare the filling. In another large bowl, place the cream cheese and stir or beat it until it is completely smooth, devoid of any lumps. Gradually add the sweetened condensed milk, whisking continuously to incorporate it thoroughly into the cream cheese. Ensure this mixture is smooth and homogenous before stirring in the vanilla extract and egg yolk. Mix these in until fully integrated.
Assembling the Bars: Remove the partially baked base from the oven. Pour the cream cheese mixture over the warm base, using a spatula to spread it evenly across the surface. Scatter the blueberries evenly over the cream cheese layer. Crumble the remaining oat mixture over the top of the blueberries and press down lightly to form a textured top layer.
Final Baking: Return the pan to the oven and continue to bake for an additional 20-25 minutes, or until the edges are golden brown and the top is slightly firm to the touch.
Cooling and Cutting: Once baking is complete, remove the pan from the oven and allow the bars to cool completely in the pan on a wire rack. This will prevent the bars from breaking when cutting. Once cooled, lift the bars out of the pan using the edges of the parchment paper as handles. Transfer to a cutting board and cut into desired sizes.
Storage: Store the cut bars in an airtight container, separating layers with parchment paper to prevent sticking. They may be refrigerated to maintain freshness for up to five days. If desired, bars can also be frozen for longer storage.