Combine water, sugar, and yeast in a bowl. Let rest until foamy, about 5 minutes.
Add melted butter, 2 cups flour, and salt to the yeast mixture. Stir with a wooden spoon to form a very sticky dough. Dust your work surface with remaining ½ cup flour.
Turn dough out onto the floured counter. Knead, folding in the excess flour as needed, until dough is soft, slightly sticky, and elastic. Place in a greased bowl. Cover and let rise in a warm place until doubled in volume, about 1½ hours.
Combine sugar and most of the sea salt together in a bowl. Mix, taste, and add more salt as needed.
Butter a 12-cup muffin tin. Spoon some of the seasoned sugar into the cups and shake to coat. Turn tin over and return excess sugar to the bowl.
Transfer dough onto a floured surface and press into a rough rectangle. Roll dough into a rectangle about ⅛ to ¼-inch thick. Grate cold butter onto the dough, leaving a 1-inch border. Flatten butter using lightly floured hands. Fold rectangle widthwise into thirds. Press gently to square out the edges. Place dough onto a silicone-lined baking sheet. Wrap in plastic and refrigerate for 30 minutes.
Roll dough into a large rectangle again, pulling and stretching the corners as needed. Grate the second stick of butter over the surface. Pat down with floured fingers and fold into thirds. Roll back out into a rectangle and fold into thirds. Repeat rolling and folding one more time. Wrap in plastic and refrigerate for at least 1 hour.
Preheat the oven to 375° F (190° C).
Sprinkle a generous amount of the seasoned sugar onto your work surface. Place dough onto the sugar and sprinkle more sugar on top. Roll into a large rectangle about 1/8- to 1/4-inch thick, turning and topping with sugar between rolls.
Use a pizza cutter to trim away uneven edges. Cut dough into 12 even pieces. Sprinkle more sugar on top. Lightly pinch each pastry into a crown shape by bringing all four corners to the center; place into the muffin cups. Sprinkle more sugar on top. Let rest for 10 minutes.
Bake in the preheated oven until browned and puffed, 25 to 30 minutes. Transfer onto a cooling rack while still hot. Let cool for 15 minutes.