In the large bowl of a stand mixer, combine milk, yeast, and sugar. Let stand until yeast softens, 5 to 7 minutes. Add table salt, chives, thyme, 2 eggs, and 1/3 cup butter and mix on low speed with dough hook until blended.
Blend in 5 cups flour. Mix on medium until dough is smooth, stretchy, and pulling away from inside of bowl, 10 minutes. Add just enough flour so dough is only slightly tacky. Cover and let rise in a warm place until doubled, about 1 1/4 hours.
Butter 20 muffin cups. Punch down dough. On a large, lightly floured work surface, roll out dough to an even 30- by 9-in. rectangle. Brush with 1 tbsp. butter.
Cut dough into 6 long strips, each 1 1/2 in. wide. Stack strips, then cut stack in half crosswise. With a serrated knife, gently cut each stack into 10 portions. Arrange each with a set of edges up in a muffin cup so you see all the layers.
Let rise at room temperature, loosely covered, until puffy, 45 minutes. Meanwhile, preheat oven to 350°. Beat remaining egg, then gently brush over tops and sides of rolls. Sprinkle with sea salt.
Bake rolls until golden brown, 20 to 25 minutes, switching pan positions halfway through baking. Let cool in pans on a rack 5 minutes, then gently lift out to racks and serve warm or cool.
Make ahead: Prepare through step 4, then wrap loosely with plastic wrap and chill overnight. Allow 1 1/4 hours for second rise.
Note: Nutritional analysis is per roll.