Combine 2 cups flour, sugar, undissolved yeast and salt in a large mixer bowl. Heat milk, water, and 1/4 cup butter until very warm (120 to 130 degrees F). Stir into flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg and 1/2 cup flour; beat 2 minutes at high speed. Stir in enough remaining flour to make a soft dough. Knead on lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; let rest 10 minutes. (Or, if desired, place dough in a greased bowl, cover with plastic wrap, and allow to rise in refrigerator for 12 to 24 hours.)
In a small small saucepan over low heat, heat the butter until just melted. Remove from heat and add in garlic. Set aside for 3 minutes. Strain the garlic from the butter using a fine mesh strainer. Stir in basil, thyme and parsley and set aside while you cut the dough.
Divide dough in half; roll each half to a 12-inch square, about 1/4-inch thick. Cut each into 6 (12 x 2-inch) strips. Cut each strip into 3 (4 x 2-inch) rectangles.
Brush each rectangle with melted butter. (If your butter has started to solidify, gently warm it over very low heat until it melts completely.) Crease rectangles slightly off center with dull edge of knife and fold at crease. Arrange in rows on greased baking sheets, with shorter side of each roll facing down. Allow 1/4-inch of space between each row. Cover; let rise in warm, draft-free place until doubled in size, about 30 minutes. Allow remaining herb butter to solidify.
Bake in preheated 400 degrees F oven for 13 to 15 minutes or until done. Remove from sheets; cool on wire rack. Gently warm the remaining herb butter over low heat and brush the rolls once again and sprinkle with sea salt.
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