Step 1In a large saucepan, combine the milk, cream and three-fourths cup sugar. Split and scrape the vanilla bean, and add the seeds and pod to the milk mixture. Stirring frequently, bring the mixture to a boil and then remove from the heat.
Step 2In a medium bowl, whisk together the egg yolks and the remaining 4 teaspoons sugar in a medium bowl. Temper the eggs by slowly pouring half of the hot milk mixture into the bowl with the eggs, whisking constantly. When combined, slowly add the egg mixture to the saucepan while whisking. Cook the mixture over low heat, whisking constantly until the mixture begins to thicken, about 5 to 7 minutes.
Step 3Immediately remove the pan from the heat and pour the mixture into a bowl set over an ice bath. Stir until the mixture is cool. Strain into a medium bowl. Stir in the ground coffee, Trablit and espresso. Refrigerate the mixture until chilled. Place the mixture in an ice cream maker and proceed according to the manufacturer's instructions. Store in the freezer up to one week.
Step 1Combine the butter, cocoa powder and powdered sugar in the bowl of a stand mixer. Using a paddle attachment, mix until just combined and there are no streaks of butter. Alternatively, combine the butter, cocoa powder and powdered sugar in a large bowl and blend with a hand mixer until no streaks of butter remain.
Step 2In a small bowl, beat the egg. Add half of the beaten egg (discard the other half) to the butter-cocoa-sugar mixture and mix until smooth.
Step 3In a small bowl, combine the salt and flour. Add them to the butter mixture and mix on medium-low speed until the flour is incorporated; be careful not to overmix.
Step 4Form the dough into a disk and wrap in plastic wrap. Refrigerate at least two hours, or overnight.
Step 5Heat the oven to 325 degrees. Remove the dough from the refrigerator and allow to sit for about 10 minutes. Roll the dough out to about one-eighth-inch thick. Cut out eight 4-inch rounds and press each round into an individual 3-inch tart mold. You will have some dough left over. Chill the molds until firm, 30 minutes to an hour. Trim the excess dough from the tops.
Step 6Place the shells on a baking sheet. Weight each of the shells with pie weights and bake for 12 minutes. Remove the weights and continue to bake an additional 10 to 12 minutes until the shell is set and firm. Allow to cool and set aside.
Step 1Heat the oven to 325 degrees. Roast the walnut halves for 10 to 15 minutes until toasted and aromatic. Set aside. (Leave the oven on at 325 degrees for baking the tarts.)
Step 2In a small saut? pan over medium-low heat, cook the butter until deep brown, 5 to 7 minutes. Remove from the heat and allow to cool for 10 minutes.
Step 3In a medium bowl, whisk the eggs and yolk until lightly frothy. Stream in the warm butter while whisking the eggs until incorporated. Stir in the corn syrup, brown sugar, rum, vanilla extract and salt until combined and the mixture is smooth.
Step 4Fill the tart shells loosely with walnuts, 3 to 4 walnuts per shell, and pour in the praline filling to the brim of each tart shell. Bake at 325 degrees for 20 to 25 minutes until the top is a light golden-brown. Serve warm with espresso ice cream.