Combine yeast, warm water, and 2 tsp. sugar in bowl of a heavy-duty electric stand mixer; let stand 5 minutes. Stir in eggs, next 3 ingredients, 3 cups flour, and remaining sugar. Beat dough at medium speed, using paddle attachment, until smooth. Gradually beat in remaining 3 to 3 1/2 cups flour until a soft dough forms.
Turn dough out onto a well-floured surface, and knead until smooth and elastic (about 8 to 10 minutes), sprinkling surface with flour as needed. Place dough in a lightly greased large bowl, turning to grease top. Cover and let rise in a warm place (85º), free from drafts, about 1 hour or until doubled in bulk.
Punch dough down; turn out onto a lightly floured surface. Divide dough in half.
Roll each dough half into an 18- x 9-inch rectangle; sprinkle cheese evenly onto each dough rectangle. Starting at 1 short end, tightly roll up each rectangle, jelly-roll fashion, pressing to seal edges as you roll. Pinch ends of dough to seal, and tuck ends under dough. Place each dough roll, seam side down, in a lightly greased 9- x 5-inch loaf pan. Brush tops with oil. Cover and let rise in a warm place (85º), free from drafts, 1 hour or until doubled in bulk.
Preheat oven to 375º. Bake 25 to 30 minutes or until loaves are deep golden brown and sound hollow when tapped. Remove from pans to a wire rack, and brush loaves with melted butter. Let cool completely (about 1 hour).