Mix 2 cups of the flour, granulated sugar, salt and yeast in large bowl. Add milk, 1/3 cup butter and the egg. Beat with electric mixer on low speed 1 minute, scraping bowl frequently. Beat on medium speed 1 minute, scraping bowl frequently. Stir in remaining flour, 1 cup at a time, to make dough easy to handle.
Place dough on lightly floured surface; gently roll in flour to coat. Knead about 5 minutes or until smooth and springy. Place dough in greased large bowl, turning dought to grease all sides. Cover and let rise in warm place about 1 1/2 hours or until double. (Dough is ready if indentation remains when touched).
Grease rectangular pan, 13 x 9 x 2 inches. Heat brown sugar and 1/2 cup butter to boiling in 1 quart saucepan, stirring constantly; remove from heat. Stir in corn syrup; cool 5 minutes. Pour into pan. Sprinkle with pecan halves.
Gently push fist into dough to deflate. Pat or roll into 15 x 10 inch rectangle. Spread with 2 tablespoons butter sprinkle with filling. Roll up tightly, beginning at 15 inch side. Pinch edge of dough into roll to seal. Stretch and shape to make even. Cut into 15 1-inch slices. Place slightly apart in pan.
Cover unbaked rolls tightly and immediately refrigerate at least 12 hours (to allow for rising) but no longer than 48 hours.
Heat oven to 350 degrees. Uncover and bake 30 to 35 minutes or until golden brown. Immediately place heatproof serving plate upside down onto pan; turn plate and pan over. Let pan remain about 1 minute so caramel can drizzle over rolls.
***Note*** to bake immediately ater placing sliced dough in pan, let rise uncovered in warm place about 30 minutes or until doubled. Bake as directed above.