To prepare dough: Mix whole-wheat flour, all-purpose flour, butter, cream cheese and oil in a large bowl with a wooden spoon just until a coherent dough forms. Refrigerate the dough for 30 minutes to reduce its stickiness.
Position rack in lower third of oven; preheat to 350°F.
Roll the dough (it will be soft) into a 15-inch log. Cut the log in half, then cut each half into quarters, then cut the quarters into thirds to yield 24 equal portions, about 1 tablespoon each. Press each piece of dough into a mini muffin cup, making a well in the center and pressing the dough up the sides of the tin to form a tartlet shell.
To prepare filling: Combine egg, pecans, brown sugar, butter and vanilla in a large bowl. Divide the filling evenly among the 24 tartlet shells.
Bake the tartlets for 10 minutes. Reduce the oven temperature to 325° and bake until the filling is puffed and the crust is lightly golden, 10 to 12 minutes more. Let cool in the pans on a wire rack for 10 minutes. Turn the tartlets out and let cool completely, about 30 minutes.