Fresh Cavatelli With Garlic Tomato Sauce

Stir flour, ½ cup plus 1 tablespoon water, and ¼ teaspoon salt in a large bowl until crumbly pieces of dough form. Transfer to a work surface. Using your hands, press together dough pieces and remaining dry flour until a mass forms. Knead dough until uniform, smooth, and firm, 5 to 7 minutes. Wrap tightly in plastic wrap; let rest at room temperature for at least 1 hour and up to 3 hours.

Meanwhile, make the sauce: Place oil and garlic in a saucepan over medium-low. Once garlic starts to sizzle, reduce heat to low. Cook, stirring occasionally, until garlic is golden in spots, 10 to 12 minutes. Add shallots and ¼ teaspoon salt; cook, stirring often and lightly mashing most garlic cloves with a fork, until shallots are very tender, about 10 minutes.

Drain tomatoes over a medium bowl or liquid measuring cup; reserve ½ cup liquid. Place drained tomatoes in a large bowl and gently crush with your hands. Stir tomatoes into garlic mixture. Bring to a simmer over medium-low. Partially cover; cook, stirring occasionally and mashing tomatoes lightly with a wooden spoon, until sauce has thickened slightly, 15 to 20 minutes. Add reserved ½ cup liquid; cook, partially covered, stirring occasionally, for 10 minutes. Stir in oregano and remaining ¾ teaspoon salt. Remove from heat.

Bring a large pot of generously salted water to a boil over high. Lightly dust a baking sheet with flour. Unwrap dough and cut into 4 pieces. Place 1 piece on a work surface; rewrap remaining pieces.

Shape cavatelli: Roll dough into a ½-inch-thick rope. Cut rope crosswise into ½-inch pieces; pieces will flatten as you cut. Working with 1 piece at a time, hold a table knife flat on top, blade parallel to cut sides. Place index and middle fingers on top of knife. Firmly press into dough and roll knife until dough comes off in the shape of a hot dog bun. Place on prepared baking sheet. Repeat with remaining dough.

Cook cavatelli in boiling water, stirring occasionally, until just tender, 5 to 7 minutes. Drain, reserving ¼ cup cooking water. Add cooked cavatelli and reserved cooking water to tomato sauce. Place saucepan over low heat and cook, stirring constantly, until pasta is coated in sauce, 1 to 3 minutes. Top with cheese, if desired.