Step 1For the crust, combine the flour, 2 tablespoons sugar, salt and lime zest in bowl. Cut the butter into half-inch slices and add to the flour mixture. Using your fingertips, a pastry blender or two knives, work the butter into the flour to make a fine crumbly mixture that starts to hold together. Sprinkle with 1 tablespoon cold water and toss until dough hangs together. Gather the dough into a ball, wrap it in plastic wrap and chill 30 minutes.
Step 2Unwrap the dough and press it evenly into the bottom and up the sides of a 9-inch tart pan with a removable bottom. (If the dough gets too soft to handle, return it in the pan to the refrigerator for about 5 minutes.) Place the dough-lined pan in the freezer for 30 minutes.
Step 3While the dough freezes, combine the milk, cream and 4 tablespoons sugar in a heavy saucepan. In a medium bowl, whisk the egg yolks with the remaining 2 tablespoons sugar and the cornstarch.
Step 4Bring the milk mixture just to a boil over medium heat. Ladle about one-third into the egg yolks and whisk until smooth, then beat the egg mixture into the milk mixture in the pan, whisking until it thickens and just comes to a boil, about 1 minute.
Step 5Remove from heat and stir in the vanilla. Transfer the mixture to a clean bowl and lay plastic wrap directly onto the surface. Chill until completely cold.
Step 6Heat the oven to 375 degrees. Bake the tart shell in the lower third of the oven until golden brown, 20 to 25 minutes. Cool completely on a rack.
Step 7Rinse the berries and hull if necessary. Pat completely dry.
Step 8Scrape the pastry cream into the cooled tart shell and smooth the surface. Carefully arrange berries on top, in alternating rings if using more than one variety.
Step 9Bring the lime marmalade to a simmer in a small saucepan and heat until melted. Brush lightly over the berries. Chill the tart at least 1 hour but no more than 4 before removing the ring from the pan and cutting the tart into wedges to serve.