In large bowl, light beat one egg.
Stir in milk, yeast, sugar, and salt.
Add 1 cup of flour and 1/4 cup softened butter. Mix well.
Add remaining flour until dough chases the spoon around the bowl.
Turn out on floured board and knead, adding more flour by the tablespoonful until the dough is only slightly sticky.
Grease medium bowl. Put dough in bowl then flip dough over so that the top of dough is also lightly greased. This prevents the dough top from forming a crust.
Allow dough to rise in warm place for about 45 minutes or until double in size.
When the dough is nearly ready to be punched down, begin making the glaze and filling for the sticky buns.
In medium saucepan, add 1 stick butter, corn syrup, and brown sugar. Melt over low heat, stirring constantly. Remove glaze from heat and continue with next step.
Butter the sides of a 10-inch round casserole dish. (Square pans and cake pans also work well, as long as they are deep so that the glaze doesn’t boil out into the oven.) Pour about a cup of the glaze onto the bottom of the dish. Sprinkle the pecans or walnuts on the bottom.
Return to the dough, punch down dough and turn out onto lightly floured board. Quickly knead out air bubbles.
Use a rolling pin to roll dough out into a rectangle, approximately 12 by 18 inches.
Spread remaining brown sugar mixture on the dough, leaving an inch of dough around all four sides clean.
Roll up long side of dough, like a jellyroll.
Cut off an inch of dough on each end and either throw it away or give it to the kids to munch on.
Slice the dough into 9 equal pieces and arrange cut side down in the casserole dish.
Cover sticky buns with plastic wrap and let them rise a second time in a warm place for about 30 minutes.
Remove plastic wrap and bake sticky buns at 375 degrees F for about 25 minutes.
Remove sticky buns from oven and carefully turn them out onto a large dish.
Let cool for about 15 minutes before eating.