Combine milk, sugar, and yeast in a large bowl; stand 5-10 minutes until foamy. Whisk in melted butter, egg, and thyme.
Stir in flour and salt until soft dough forms; knead on lightly floured surface 6-8 minutes until smooth and elastic.
Place in greased bowl; cover with clean kitchen towel and rise in warm place 1 hour until doubled.
Punch down; divide into 12 equal pieces. Shape smooth balls by pulling edges underneath; space evenly in greased 9x13-inch dish.
Cover with towel; rise 30-40 minutes until puffy and touching.
Preheat oven to 375°F. Brush rolls with melted butter; bake 16-18 minutes until tops are golden brown.
Remove; brush with additional butter and serve warm.