Preheat the oven to 350 degrees. Wrap the outside of a 9-inch springform pan with foil. Using a food processor, finely chop the cookies, nuts, brown sugar and 1/4 teaspoon salt. Add the butter and pulse until just combined. Press into the bottom of the prepared pan and bake until set, 10 to 12 minutes. Transfer to a rack to cool. Lower the oven temperature to 300 degrees.
Using a mixer, beat the cream cheese until softened, 2 minutes. Beat in the flour and remaining 1/4 teaspoon salt on low speed. Beat in the eggs and egg yolk, 1 at a time, on medium speed. Mix in 1 cup dulce de leche.
Pour the batter into the crust. Loosely cover the pan with foil, set in a roasting pan and pour in enough boiling water to reach a depth of 1 inch. Bake the cheesecake until set at the edges but slightly wobbly in the center, about 55 minutes.
Transfer the cake to a rack; let rest for 15 minutes. Spread the remaining 3/4 cup dulce de leche over the warm cake. Refrigerate until ready to serve, then remove the springform and slice the cheesecake.