Heat oven to 325°F. Butter an 8-inch square baking pan. Line with 2 crisscrossed pieces of parchment, buttering in between and leaving an overhang on all sides; butter the parchment.
Pulse the cookies until fine crumbs form in a food processor. Add the butter and pulse to combine. Using a straight-sided dry measuring cup, press the mixture into the prepared dish. Bake until firm, 7 to 9 minutes.
Meanwhile, beat the cream cheese in a large bowl with an electric mixer on medium-high, scraping down the side of the bowl as necessary, until smooth, 1 to 2 minutes. Add the sour cream and beat until smooth. Add ¾ cup of the dulce de leche and beat to combine. Beat in the eggs and vanilla, scraping down the sides twice. Pour over the cooked crust.
Bake, rotating once, until the cheesecake is almost set but jiggles slightly in the middle, 35 minutes. Cool completely in the pan, then refrigerate for at least 2 hours.
Spoon the remaining ¼ cup dulce de leche over the cheesecake. Chill until set, about 15 minutes but up to 2 days.
Sprinkle with the salt just before serving.
Tip: It’s important when making cheesecake that all of the ingredients are at room temperature. This will insure that everything thoroughly mixes together without any lumps.