Preheat oven to 400°.
Combine first 4 ingredients in a medium bowl; beat at medium speed of a mixer until light and creamy. Add vanilla and 1 egg; beat well. Gradually add flour, beating at low speed until moist. Press mixture gently into a 5-inch circle on heavy-duty plastic wrap; cover with additional plastic wrap. Chill 1 hour.
While dough chills, bake sweet potatoes. Bake at 400° for 55 minutes or until very tender. Cool. Reduce oven temperature to 350°. Peel potatoes; place potato pulp, brown sugar, and next 8 ingredients (brown sugar through eggs) in a large bowl. Beat at medium speed of a mixer until smooth; set aside.
Roll dough, still covered, into an 11-inch circle. Remove 1 sheet of plastic wrap, and fit dough into a 9-inch tart pan coated with cooking spray. Remove top sheet of plastic wrap. Spoon potato mixture into prepared crust. Combine 2 teaspoons water and egg white, and brush edges of dough with egg white mixture. Sprinkle potato mixture with chopped pecans. Bake tart at 350° for 1 hour or until puffy and set. Cool on a wire rack.