1. In a large bowl, sprinkle yeast over 1/4 cup cool (70?) water. Let stand until dissolved, 5 minutes. Stir in sugar, table salt, herbs, butter, whole egg, and milk; add 3 1/4 cups flour and stir to moisten.

2. Knead dough on a lightly floured board until elastic and not sticky, 15 minutes; add flour as needed to prevent sticking. Shape into 12 equal balls; place in a well-buttered 9- by 13-in. pan.

3. Let dough rise in a warm place until doubled, 45 to 60 minutes. Meanwhile, preheat oven to 350?. Brush rolls with beaten egg and sprinkle with coarse salt. Bake until deep golden, 25 to 30 minutes.

Make ahead: Prepare through step 2; immediately wrap airtight (do not let rise) and chill up to 1 day. Proceed with step 3.