Dissolve yeast in milk in a large bowl; let stand 5 minutes.
Add sweet potatoes, 1 tablespoon butter, salt, and egg yolks, stirring mixture with a whisk.
Lightly spoon flour into dry measuring cups; level with a knife. Add 4 1/2 cups flour; stir until a soft dough forms.
Turn dough out onto a floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel very soft and tacky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Gently press 2 fingers into dough. If indentation remains, dough has risen enough.) Punch dough down. Cover and let rest 5 minutes.
Line 2 baking sheets with parchment paper. Divide dough into 24 equal portions. Working with 1 portion at a time (cover remaining dough to prevent drying), shape each portion into a 9-inch rope. Carefully shape rope into a knot; tuck top end of knot under roll. Place roll on a prepared pan.
Repeat procedure with remaining dough, placing 12 rolls on each pan. Lightly coat rolls with cooking spray; cover and let rise 30 minutes or until doubled in size.
Preheat oven to 400°.
Uncover rolls. Bake at 400° for 8 minutes with 1 pan on bottom rack and 1 pan on second rack from top. Rotate pans; bake an additional 7 minutes or until rolls are golden brown on top and sound hollow when tapped.
Remove rolls from pans; place on wire racks. Brush rolls with 2 tablespoons butter. Serve warm or at room temperature.