Stir together 1 1/2 cups water and salt in a spouted measuring cup until salt is dissolved. Pile flour on a work surface into an 8-inch-wide mound. Make a 3-inch-wide well in center of mound. Slowly pour water mixture into well, gradually pulling in flour from sides of well and mixing with a fork until a coarse paste forms. Using your hands, work remaining dry flour into paste until a crumbly dough forms. Knead dough until it is smooth and bounces back when pressed, about 7 minutes. Wrap dough in plastic wrap; let rest at room temperature at least 40 minutes or up to overnight. Line 2 large rimmed baking sheets with parchment paper; lightly dust with flour. Unwrap dough; divide evenly into 4 portions. Roll 1 dough portion into a 1/2-inch-thick rope on a clean work surface; keep remaining dough portions loosely covered with plastic wrap. Cut rope crosswise into 3/4-inch-long pieces. Working with 1 dough piece at a time, roll into a 3/8- to 1/2-inch-thick rope (about 5 1/2 inches long). Lightly dust a round wooden chopstick or skewer with flour. Using your thumb and index finger, gently pinch the tapered end of the pasta rope to the pointed end of the chopstick; use your other hand to gently wrap the pasta rope around the chopstick in a loose corkscrew fashion so that the pasta rope is snug against the chopstick. Gently roll the chopstick back and forth on the work surface to flatten the pasta. Slide rolled pasta (busiate) off chopstick, and place on prepared pan; lightly dust with flour to prevent sticking. Repeat process with remaining dough. Let assembled busiate stand, uncovered, at room temperature 1 hour. (To freeze shaped busiate, let dry at room temperature 6 hours; freeze in an even layer on a rimmed baking sheet until firm; transfer to a ziplock plastic freezer bag.