Preheat the oven to 350 degrees F. Line a 9x13-inch pan with parchment.
Stir the flour, oats, baking soda, salt, and both sugars together. Pour in the melted butter and vanilla and mix until the mixture clumps.
Press about two-thirds of the oat mixture firmly into the bottom of the pan. Set the rest aside for the crumble top.
Make the Filling
Whisk the pumpkin, evaporated milk, egg, egg yolk, both sugars, pumpkin pie spice, salt, and vanilla until smooth. It should look like a loose pumpkin pie filling.
Layer and Bake
Par-bake the crust for 10 minutes so the bottom sets.
Pour the pumpkin filling over the warm crust, then scatter the reserved oat mixture over the top in clumps.
Bake for another 35 to 40 minutes, until the filling is set and the crumble is golden. Cool completely before cutting into 16 bars.
Notes
Par-bake the crust: 10 minutes before the filling goes on keeps the bottom from getting soggy.
Reserve crumble: hold back about a third of the oat mixture for full coverage on top.
Cool completely: let the pumpkin layer firm up before cutting so the bands stay neat; chill if needed.
Cut cold: a sharp knife wiped between cuts shows off the three stripes.