For the crust:
For the filling:
Preheat the oven to 350°F. Place the cookie crumbs, sugar, and melted butter in a medium bowl and stir with a fork until evenly moistened. Press the mixture onto the bottom of a greased 9-inch springform pan. Bake until golden brown and crispy, about 10 minutes. Cool completely. Reduce the oven temperature to 325°F.
In the bowl of an electric mixer using the paddle attachment, beat together the goat cheese, cream cheese, and buttermilk until smooth and fluffy, about 4 to 5 minutes. Gradually beat in the sugar until smooth. Beat in the eggs one at a time. Add the lemon juice and zest. Pour half the filling into the springform pan with the prepared crust. Sprinkle half the currants over the batter. Pour over the remaining batter and scatter the rest of the currants. Dust the top with the togarashi spice.
Wrap the bottom of the springform pan with aluminum foil to prevent water seepage. Place the pan inside a large roasting pan. Pour enough hot water into the roasting pan to have it come a third of the way up the sides of the cake pan. Bake for 1 hour and 20 minutes. The cake will be slightly puffed when done.
Remove the cake pan from the water bath. Allow it to cool to room temperature, then chill in the refrigerator for at least 2 hours. To serve, cut around the sides of the cake pan and release the side ring. Slide the cheesecake onto a serving platter. Cheesecakes can hold for up to a week in the refrigerator, tightly wrapped.
Makes 8 to 10 servings