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Preheat oven to 350ºF and grease a 9x13 inch baking pan.
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Cream the sugar and butter together until light and fluffy.
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Add the eggs, one at a time, and mix thoroughly. Scrape down sides as needed.
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Mix in milk and vanilla.
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In a medium bowl, combine salt, baking soda, flour, and oats.
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Add the dry mixture to the wet mixture, 1/2 cup at a time.
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Press 2/3 of the cookie dough into the prepared pan.
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Transfer the Dulce de Leche to a medium, microwave-safe bowl and microwave on high for 60 seconds, stirring every 15 seconds.
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Spread the Dulce de Leche over the cookie dough in the pan. Top with spoonfuls of the remaining cookie dough. {There won't be enough dough to cover the entire pan, but after it's cooked, it will look nice and pretty with the Dulce de Leche peeking through.}
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Bake for 25 minutes, checking at about the 20 minute mark. If it's getting to browned by then, place some aluminum foil over the top of it.
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Let cool completely before serving, to let the insides firm up. {It tastes better completely cooled, too. The Dulce de Leche is a lot sweeter.}