Ingredient Note: Whole-wheat pastry flour is milled from soft wheat. It contains less gluten than regular whole-wheat flour and helps ensure a tender result in delicate baked goods while providing the nutritional benefits of whole grains. Available in large supermarkets and in natural-foods stores. Store in the freezer. Tip: To separate eggs safely: Use an egg separator, an inexpensive gadget found in cookware stores; separating eggs by passing the yolk back and forth between pieces of eggshell or your hands can expose the eggs to bacteria.
To prepare crust: Whisk whole-wheat flour, all-purpose flour, 2 tablespoons sugar and salt in a medium bowl. Cut in butter with a pastry blender or your fingers until the mixture resembles coarse crumbs with a few larger pieces. Add oil and stir with a fork to blend. Mix 1/4 cup water, egg yolk and 1 teaspoon lemon juice (or vinegar) in a measuring cup. Add just enough of the egg yolk mixture to the flour mixture, stirring with a fork, until the dough clumps together. (Add a little water if the dough seems too dry.) Turn the dough out onto a lightly floured surface and knead several times. Form the dough into a ball, then flatten into a disk. Wrap in plastic wrap and refrigerate for at least 1 hour.
Preheat oven to 425°F. Line a baking sheet with parchment paper or foil and coat with cooking spray.
To prepare filling & assemble tart: Spread almonds in a small baking pan. Bake until light golden and fragrant, about 5 minutes. Let cool. Combine whole-wheat flour, 1/4 cup sugar (or Splenda) and the toasted almonds in a food processor or blender; process until the almonds are ground.
Roll the dough into a rough 13- to 14-inch circle on a lightly floured surface, about 1/4 inch thick. Roll it back over the rolling pin, brush off excess flour, and transfer to the prepared baking sheet. Spread the almond mixture over the pastry, leaving a 2-inch border all around. Toss berries with the remaining 3 tablespoons sugar (or Splenda) and 2 teaspoons lemon juice in a large bowl; spoon over the almond mixture. Fold the border up and over the filling, pleating as necessary. Blend the reserved egg white and 1 tablespoon water with a fork; brush lightly over the tart rim. Sprinkle with the remaining 1 teaspoon sugar.e the tart for 15 minutes. Reduce oven temperature to 350°F and bake until the crust is golden and the juices are bubbling, 30 to 40 minutes. Leaving the tart on the parchment (or foil), carefully slide it onto a wire rack. Let cool.
Shortly before serving, melt jam in a small saucepan over low heat; brush over the berries. Cut the tart into wedges.