Arrange melon in a shallow dish. In a bowl combine Muscat de Beaumes-de-Venise and 5 tablespoons of the sugar. Pour over melon and chill for 24 hours. Drain.
Prepare the pastry: In a bowl combine flour and 1 tablespoon of sugar with salt. Add butter and blend until mixture resembles coarse meal. In another bowl whisk together the egg and milk. Add flour mixture and stir until mixture forms a soft dough. Chill, covered, 2 hours.
Pre-heat oven to 350 degrees. Roll out the dough into a 1/8-inch thick round on a floured surface. Place the dough onto a 10-inch tart pan with a removable bottom. Prick the pastry shell all over with a fork and cover with a sheet of buttered wax paper. Fill the shell with dried beans, and place in the pre-heated oven for 8 minutes. Remove the beans, prick again with a fork, and bake for another 10 minutes or so, or until the tart is golden brown. Remove and let cool.
Prepare the apricot glaze: In a small, heavy saucepan, combing the apricot jam with 1 tablespoon of sugar and 2 tablespoons of Muscat de Beaumes-de-Venise. Bring to a boil and boil for 1 minute. Strain.
To assemble: Brush a thin layer of the hot apricot glaze over the bottom of the tart shell. Then place a thin layer of pastry cream (you might have a bit left over). Arrange the melon slices over the pastry cream. Warm the remaining apricot glaze and brush over the melon slices. Let the tart rest for at least 15 minutes.
Garnish the center of the tart with mint leaves. Include a mint leaf with each serving. If desired, serve a chilled glass of the melon marinade with the tart.