To make dough: Beat the cottage cheese, cream cheese, granulated sugar, oil, butter and vanilla in a medium bowl with an electric mixer until light and fluffy. Mix together flour and salt and add to the cheese mixture; stir with a wooden spoon until just blended. Wrap dough in wax paper, then in plastic wrap, and chill 2 to 3 hours or preferably overnight.
To make filling: Stir together brown sugar, Grape-Nuts, walnuts and cinnamon in a small bowl. Cover and set aside.
Set oven rack in upper portion of oven; preheat oven to 350 °F. Coat two baking sheets with cooking spray or line with parchment paper.
To form and bake rugelach: Divide the dough into four equal parts. Roll each portion on a lightly floured surface into a 10-inch-diameter circle. (Keep the remaining dough chilled until ready to use.) Sprinkle with one-quarter of the brown-sugar mixture and 2 tablespoons currants, pressing slightly so that the filling adheres. Cut the circle into 8 wedges. Beginning at the widest end, roll up each wedge and curve into a crescent. Place on a prepared baking sheet. Repeat with the remaining dough.
Bake until tops are light brown, 20 to 25 minutes. Immediately transfer to a rack and let cool.