Make 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 caramelized onion: In a skillet heat the olive oil until hot and cook the onions, stirring constantly, until golden. Remove from heat and let cool, set aside.
To assemble tartlettes: Take 8 small pie tins, brush with butter and liberally sprinkle with corn meal. 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 or the tomatoes will bleed through bottom. Place disk in pie tin and repeat until all 8 are done. Place dough in tins on baking sheets.
Preheat oven on to 375 degrees F.
Brush bottoms of dough shell with 1 teaspoon of mustard. In the following order place into each shell: 2 tablespoons of shredded cheddar cheese, 1 tablespoon caramelized onion, 4 slices of tomato, salt and pepper, and 1 teaspoon of olive oil.
Fold in the tops of the flaps of extra dough around the tomatoes, brush dough with egg whites. Bake for 30 to 45 minutes. Right before serving, garnish top with basil. Serve at room temperature.