In a stand mixer, dissolve yeast in warm water. Let stand 5 minutes, then on low speed, mix in melted butter, honey, eggs, and salt until smooth. Increase speed to medium, and add flour 1 cup at a time until mixture forms a soft dough. Knead dough at medium speed until smooth and elastic, about 3-4 minutes. Form dough into a ball and place in a greased bowl, turning once to grease top. Cover top with plastic wrap and let rise in a warm place until doubled, about 2 hours.
Once dough is doubled, punch it down to deflate it. Cover bowl with plastic wrap and let rise a second time until doubled, about 1 hour.
Punch dough down, and turn onto a floured surface. Divide dough into 3 equal pieces. Roll each piece into a 12 in long rope. Place dough ropes side-by-side, and working from the top to the bottom, braid the dough ropes. Pinch edges to seal and tuck underneath braided dough. Transfer bread to a parchment-paper lined baking sheet. Cover bread with plastic wrap and let rise until doubled, about 30 minutes.
Bake challah at 375F 30-35 minutes, or until golden brown. Brush top with additional butter and sprinkle with sea salt while warm. Let cool on a wire cooling rack 15 minutes before slicing. Serve warm.
Store challah in an airtight container at room temperature up to 2 days.