In the bowl of a stand mixer fitted with the dough hook, add the water, sugar, and yeast. If using active dry yeast, let the mixture stand until foaming and bubbly, about 5 minutes. If using instant yeast, proceed with the recipe.
Add 2 cups of the flour, 2 tablespoons of the chopped rosemary, and the salt, and mix to combine.
With the mixer on medium speed, gradually add flour until a soft dough is formed that clears the sides and center/bottom of the bowl and knead for 4 to 5 minutes. The exact amount of flour will depend on several factors, so judge the amount of flour needed by the look and feel of the dough. The dough should be slightly tacky to the touch and form a ball without leaving a lot of doughy residue on your fingers.
Transfer the dough to a lightly greased or oiled bowl, cover, and let rise until doubled in size, approximately 1 to 2 hours.
Line a half sheet pan with parchment paper, lightly grease with cooking spray, and set aside.
Turn the dough onto a lightly greased countertop and divide in half.
With lightly floured or greased hands, take each piece of dough and fold it in half, pressing the bottom seam to seal. Move your hands to the rough ends and do the same. Continue this process until a taut loaf is formed, making sure to pinch any seams to seal.
Place the loaves equal distant apart on the prepared baking sheet with plenty of room in between them for rising and baking.
Use a sharp razor blade or baking lame to gently slash 2 to 3 lines across the top of the loaves.
Brush the melted butter evenly across the top of the loaves. Continue brushing on the butter until it is gone (the loaves will be well-saturated).
Sprinkle the remaining chopped rosemary and a pinch or two of coarse salt over the top of the loaves.
Cover and let rise until puffy and nearly doubled, 45 to 60 minutes.
Toward the end of rising time, preheat the oven to 425 degrees.
Bake for 20 to 22 minutes until golden.
Notes
If the bread is flattening while rising or baking, try adding a bit more flour to the dough and/or letting the loaves rest for 15 minutes after shaping and then taking each loaf and reshaping into a taut loaf before letting the loaves rise fully to bake.