In a food processor combine the ground pecans, flour, salt, and sugar. Add the butter and process until the mixture resembles coarse crumbs. Pour in the egg white and blend it in to bind the dough until it holds together without being too wet or sticky. Squeeze a small amount of dough together, if it is crumbly, add the ice water, 1 tablespoon at a time. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.
Lightly coat a 12-cup muffin tray with nonstick spray. Roll out the dough on a lightly floured surface to about a 2 foot square, then use a small bowl 3-inches in diameter or a large 3-inch ring mold as a guide to cut out circles. They should be slightly larger in diameter than the muffin tin hole, so when pressed in, the edges come half-way up the sides of the tin.
Preheat oven to 350 degrees F.
In a large mixing bowl, mix the eggs until frothy then blend in sugars. Stir in the melted butter, vanilla, syrup and salt until well blended. Arrange the pecans on the bottoms of the tart shells. Pour in the filling to fill the shells almost to the top. Bake until the filling is set and slightly puffed, about 25 to 30 minutes. Test for doneness by sticking a thin knife in the center of the pie, if it comes out pretty clean, you're good to go. Transfer the pies to a rack and cool.
While the pie is baking, make the Sweet Tea Caramel Sauce. Begin my making the tea. Bring 2 cups of cold water to a boil in a large heavy saucepan. Add the tea bags, cover and let steep for 20 minutes. Remove the tea bags (squeeze them out) and then return to a simmer until it has reduced by half - so you have 1 cup of really strong tea remaining. Add the 1/2 cup of sugar to the saucepan and continue to simmer over medium heat. Cook, swirling the pot around, until the mixture is a deep caramel color and looks like syrup, about 10 minutes. Carefully pour in the cream, be careful as it will bubble up, and continue to cook for 1 more minute. Serve with individual pecan pies and a scoop of vanilla bean ice cream.