Place the flour and sugar in the bowl of a food processor. Pulse several times to combine the ingredients, then add the butter and pulse a few more times until the mixture resembles coarse cornmeal. A few larger pieces are fine.
In a liquid measuring cup, briefly whisk together the yolk, water and vanilla. With the machine running, pour the liquid in until the dough has just barely formed. Turn the dough out onto plastic wrap and flatten into a disc. Wrap and chill for at least 2 hours.
On a lightly floured surface, roll the dough into a circle approximately 12 inches in diameter. Roll the dough around the rolling pin and then unroll it into a 9-inch fluted tart pan, leaving slack so the dough can settle into the flutes. Gently shape the dough to the side of the pan and trim away excess dough (if possible, leave 1/4 inch overhang to account for any shrinkage while baking).
Chill the dough for at least 15 minutes.
Meanwhile, preheat the oven to 375 degrees F. Use a fork to prick numerous holes in the dough to prevent air bubbles. Add a layer of aluminum foil and top with dried beans. Place the tart pan on a baking sheet and bake for approximately 20 minutes, removing the beans and foil halfway through, until the dough has just firmed up on the bottom. Allow to cool.
Prepare the panna cotta:
Place the gelatin in a large bowl with the lukewarm water to soften for 5 minutes.
In a medium saucepan, bring the cream, milk, sugar, and vanilla to a simmer over medium-high heat, stirring until the sugar has dissolved. Remove from the heat and pour into the bowl with the gelatin, whisking until smooth. Carefully pour into the tart shell and place in the refrigerator to chill until the panna cotta sets, 2-4 hours. (Note: To avoid spills, you might want to place the tart on a shelf in the refrigerator and pour the panna cotta mixture into the shell there so it doesn’t need to be transferred while the mixture is in liquid form. It will be easier to do this if pouring from a bowl with a spout).
One the panna cotta is firm, gently layer the currants on top. You can either remove the currants from the stem, or leave them on as garnish. While this makes for a beautiful presentation, it will require that you remove the currants while slicing and serving the tart.
Mixed currants, while beautiful, are difficult to locate. You can substitute a single color (red, white, etc), or use a different fruit altogether. For example, this tart would be beautiful with blueberries or raspberries.I used a Wilton 9x1-inch tart pan with a removable bottom.