Preheat oven to 350°F. Line a 9x9” square pan with foil and spray well with cooking spray. You can use parchment in place of foil, if you prefer.
Cream butter and sugar in a mixer fitted with the paddle attachment. Cream until smooth, just a minute or so. Beat in egg, vanilla, baking soda, and salt. Mix in flour then slowly mix in oats.
Press half the mixture into the bottom of the prepared pan. It will be a thin layer. The dough is sticky so I suggest spraying your hands with cooking spray to help the dough not stick to you.
Place dulce de leche in a small microwave safe bowl. Heat about 45-60 seconds in the microwave, then stir until smooth. You just want to make it spreadable, not too liquidy. In it’s normal form it would be too hard to spread over the raw dough.
Pour the dulce de leche evenly over the bars, trying to keep a 1/4” border around the edges of the pan.
Use two spoons to scoop the remaining dough all over the top of the bars. Press slightly with your fingers to smooth the lumps of dough. It will not completely cover.
Bake for about 23-28 minutes, until the top of the bars are golden brown. The pan will still be jiggly. Let them cool completely before attempting to slice. They’ll be gooey!
Store in an airtight container for up to 4 days or freeze in a single layer for up to one month.