Step 1 To make the sealing dough, mix together the flour, eggs, a pinch of salt, the sugar and herbs in the bowl of an electric mixer until a stiff dough forms. Cover it with plastic wrap and let it rest for 1 hour.
Step 2 Heat the oven to 350 degrees. Season the chicken inside with salt and pepper. Line the cocotte with hay, creating a nest-like effect, as far up the sides of the pot as possible. Place a shallow rack in the center and put the chicken on it. Add the water, pouring around the sides.
Step 3Roll out the sealing dough into a long, 2-inch-wide strip that can fit around the edge of the pot. Press the strip of dough onto the edge of the pot, circling the entire rim, and then place the lid on. Press down; the dough acts as a seal between pot and lid. Some of the dough will be exposed; brush it with the egg wash.
Step 4Heat the filled pot on top of the stove over high heat until the pot is hot, about 2 minutes. Transfer it to the oven and bake for 1 hour and 20 minutes. Rotate the pot in the oven occasionally to heat all sides evenly.
Step 5After cooking, remove from the oven and let rest for 10 minutes to finish cooking. Take the pot to the table and remove the lid in front of your guests. Return the chicken to the kitchen to remove it from the pot. Gently wipe any hay from the chicken. Brush the chicken with the melted butter and carve into serving pieces. Season with more freshly ground pepper to taste.