Preheat the oven to 350°F. Position a rack in the center. Lightly coat an 8-inch square metal baking pan with nonstick spray, then line it with parchment paper, leaving an overhang on two opposite sides.

In a medium bowl, stir together the flour, rolled oats, brown sugar, baking soda, and salt. Add the melted butter and mix until no dry flour remains and the mixture forms damp crumbs that hold together when squeezed. Measure and reserve 1 1/2 cups of the mixture for the topping. Press the remaining mixture firmly and evenly into the prepared pan.

Bake the crust for 10 to 12 minutes, until the surface looks matte rather than wet and the edges are just beginning to turn golden. Place the pan on a wire rack and let the crust cool for about 10 minutes while preparing the filling.

Beat the softened cream cheese and granulated sugar on medium-low speed until smooth. Mix in the flour and salt. Add the egg and vanilla, then mix on low only until evenly combined, scraping the bowl as needed.

Spread the cream cheese filling evenly over the partially cooled crust without pressing into it. Scatter the reserved oat mixture evenly over the filling, breaking up any very large clumps with your fingers.

Return the pan to the oven and bake for 24 to 28 minutes. The oat topping should be lightly golden, the edges of the filling should look set and slightly raised, and the center should move as one soft unit when the pan is gently nudged rather than ripple like liquid. Do not bake until the center is completely rigid.

Cool the bars in the pan on a wire rack for 1 hour. Cover and refrigerate for at least 2 hours, or until the filling is fully firm. Lift the slab from the pan using the parchment, wipe the knife between cuts, and cut into 16 bars.