Make the tart dough: Put in the work bowl of a food processor, the flour, butter, salt and sugar. Pulse quickly until the butter is the size of peas. Add very cold, ice water in a small stream until the dough just comes together. Empty the work bowl out onto waxed paper and halve the dough. Using the ends of the paper, shape into 2 balls. Wrap in plastic wrap and place in refrigerator until ready for use.
Make the caramelized sugar: Pour sugar in heavy skillet, cook over low heat until sugar turns a medium brown. Pour caramelized sugar in a 10-inch aluminum tin or silcone mat to cool and harden. After it is cooled, break into pieces of 1-to 1 1/2-inch big. Set aside, it will be used to bake with berries.
Make fruit filling: In a large bowl, place cleaned gooseberries and blueberries. Pour lemon juice on top. Sprinkle sugar, flour and nutmeg on top of the berries (Be careful not to mix, just sprinkle on top, or fruit will be mushy if over-handled).
To assemble tartlettes: Take 8 small pie tins, brush with butter and liberally sprinkle with cornmeal. Cut dough into 8 equal pieces and put 7 back in the refrigerator (must be kept cold) roll out the dough into a 4-inch circle, it should be quite thick, you don't want it too thin. Place disk in pie tin and repeat until all 8 are done. Place all 8 tarts on sheet pan.
Preheat oven to 375 degrees F. Brush bottom of dough shell with egg whites. Gently scoop out the berries with the flour-sugar mixture on top into the shells. Place a piece of the caramelized sugar on top of berries. Fold up the sides in a circle, do not close up completely, leaving an opening. Put 1 tablespoon butter on top of each tartlette. Brush egg white on the exposed dough and bake for 45 minutes.