Whisk the eggs, egg yolks, and sugar in a medium heatproof bowl to blend. Whisk in the lime juice. Set the bowl over a large saucepan of gently simmering water. Do not let the bottom of the bowl touch the water. Whisk constantly for about 5-7 minutes until the curd thickens. Immediately pour the curd through a strainer set over a bowl to remove any lumps of egg. Add the butter to the strained curd and whisk until it is fully combined. Press a sheet of plastic wrap directly onto the surface of the curd to prevent a skin from forming. Refrigerate the curd until cold, at least 4 hours. You can make the curd up to two days ahead.

Place the flour, confectioner’s sugar and salt in a food processor. Pulse a few times to combine. Add the butter and pulse until the butter is coarsely cut in. Stir the yolk in a small bowl to break it up and add it a bit at a time, pulsing after each addition. When the entire yolk has been added, process the dough in long pulses (about 10 seconds) until the dough forms clumps. Turn the dough out onto a work surface and very lightly knead the dough just to incorporate any dry ingredients that weren’t mixed in. Do not work the dough too much.

Butter a 9 or 10-inch fluted tart pan with a removable bottom. Press the dough evenly over the bottom and up the sides of the pan. Refrigerate the dough for at least 30 minutes or longer before baking.

Preheat the oven to 375 degrees F. Pierce the tart with a fork or knife a few times to create air holes (for steam to escape). Butter the shiny side of a sheet of aluminum foil and fit the foil, buttered side down, tightly against the surface of the crust. Bake for 20-25 minutes in total. Halfway through (approximately 15 minutes) remove the foil and let the shell continue baking. The edges should have a deep golden colour when you take it out of the oven. Allow the shell to cool completely before filling.

Combine the apricot jam, water and dark rum in a small saucepan. Bring to a boil and turn the heat down to low. Let the glaze cook down until it thickens, approximately 5 minutes. Remove from heat.

Layer the lime curd over the cooled crust and top with fresh blueberries, apricot glaze, and whipped cream, if desired.