Make the ice cream: Heat the half-and-half and vanilla bean in a saucepan over medium heat, stirring occasionally to make sure the mixture doesn't scorch on the bottom. When the cream mixture reaches a fast simmer (do not let it boil), turn off the heat. Set the mixture aside to infuse for 10 to 15 minutes.
Whisk together the egg yolks and sugar in a medium bowl. Whisking constantly, slowly pour the hot half-and-half mixture into the egg yolk mixture. Return the mixture to the saucepan and cook over medium heat, stirring constantly with a wooden spoon. At 160 degrees F, the mixture will give off a puff of steam. When the mixture reaches 180 degrees F, it will be thickened and creamy, like eggnog. Test it by dipping a wooden spoon into the mixture. Run your finger down the back of the spoon. If the stripe remains clear, the mixture is ready; if the edges blur, the mixture is not quite thick enough yet. When it is ready, quickly remove it from the heat.
Immediately whisk in the peanut butter and whisk until smooth. Strain the mixture into a bowl to smooth it and remove the vanilla bean. Rest the bottom of the bowl in the ice bath and let the mixture cool, stirring often, for 2 hours. Freeze according to the directions of the ice cream machine.
Make the crusts: In a mixer fitted with a paddle attachment (or using a hand mixer), mix the flour and sugar. Add the butter and mix until coarse and sandy.
Whisk the egg yolks, cream, and vanilla together. Add to the flour mixture and mix at low speed just until combined. If the mixture seems too dry, add another teaspoon of heavy cream. Turn the dough out onto a work surface and form into a disk. Wrap in plastic wrap and refrigerate for at least 1 hour, until ready to use. (The recipe can be made up to this point and keep refrigerated for up to 2 days.)
Roll out the dough 1/8-inch thick on a lightly floured surface and cut out circles that are 2 inches larger in diameter than the mini-muffin cups.
Spray the muffin tin well with nonstick cooking spray, then gently press the dough rounds into the cups, easing the dough completely into the cups. Smooth out the folds by pressing the dough against the sides and bottoms of the cups (the walls will become a little thicker). Use your fingers to form the rim of each tartlet into an even edge, pulling or cutting off extra bits of dough, if necessary.
Spray the bottom-outside of another mini-muffin tin with nonstick spray and gently push it down into the tin with the dough rounds so that it "spoons" into the bottom cups. This will help prevent shrinkage during baking. Chill for 30 minutes.
Heat the oven to 375 degrees F.
Keeping the tins pressed together, turn them upside down on a sheet pan. Bake until the crusts are dry and golden but not brown, about 12 minutes. Let them cool upside down for 20 minutes, then invert the pans and carefully lift the top tin out, leaving the pastry cups in the bottom tin.
Meanwhile, make the filling: Melt the chocolate and butter together in the top of a double boiler set over barely simmering water, stirring frequently. When melted, remove the mixture from the heat and whisk in the eggs, sugar, vanilla, and salt.
Heat the oven to 350 degrees F.
Pour the filling into the prebaked tart shells (still in their tins) and bake for 11 to 13 minutes, until the filling is set at the edges but still a little moist in the center.
Meanwhile, make the caramel sauce: Pour the sugar into the center of a deep saucepan. Carefully pour 1/2 cup water around the sugar, trying not to splash any sugar onto the sides of the pan. Do not stir; gently draw your finger through the center of the sugar to moisten it. Over high heat, bring the mixture to a full boil and cook without stirring, swirling the pot occasionally to even out the color, until it is amber-caramel, 10 to 20 minutes. When the mixture is done, immediately remove the pot from the heat. Use a wooden spoon to slowly stir in the red wine. Set aside.
When ready to serve, arrange the tarts on serving plates. Put a dollop of the sauce on the plate on 1 side of the tart and a small scoop of the ice cream on the other side. Serve immediately.