Dough scraps left on the tray after cutting with a cutter should not be gathered into a lump and kneaded again: puff pastry layers break down, while gluten develops in cookie and tart dough, making the second batch tough. Instead, stack the scraps, press them lightly, let them rest, and roll them out one more time, or bake them in strips without rerolling to make something else.
Scraps left as dough is rolled and cut have already been worked. Each time a flour-based dough is kneaded and rolled, it develops a little more gluten; the dough becomes elastic, springs back when rolled, and turns tough when baked. When the scraps are gathered into a lump and kneaded again, that process happens one more time, and the flour dusted on during rolling also gets mixed into the dough. The result is dough that is tougher and drier than it was on the first round. That is why scraps should be brought together, not kneaded.
The problem is greater with puff pastry. Its rise depends on thin layers of fat and dough stacked on top of one another. If the scraps are formed into a lump, the layers mix together, producing a greasy piece that does not puff in the oven. The right approach is to stack the scraps with the layers horizontal: place the pieces side by side and on top of one another, press them lightly with a rolling pin, and let them rest in the cold. Then roll them out one more time; this second round will not puff as much as the first, but the layers will remain, and the cut pieces will still open up in the oven.
With cookie and tart dough, too, do not form the scraps into a lump; press them together instead. Stack the pieces, press them lightly with your palm or a rolling pin, and shape the dough into a firm disk. Since the warmth of your hand softens the dough, let it rest in the cold; it is ready to roll when it no longer springs back as you press it by hand. On the second round, use only a little flour for rolling and cut the cookies close together with a cutter so a third round of scraps is not needed. Arrange the second-round cookies on a separate baking sheet.
Some scraps can also be used without rolling them out again. Cut puff pastry scraps into strips, sprinkle cheese or sesame seeds on top, and bake them on a baking sheet; they make crisp sticks to serve with soup. If phyllo scraps are stacked and cut into thin strips, they crisp up in a pan or oven and can be sprinkled over soup or salad; with syrup or powdered sugar, they make a sweet crisp. Bake cookie scraps in small pieces and crumble them over a dessert base.
Yeast dough is different. Scraps from bread, Turkish flatbread, and savory bread rolls can be gathered and kneaded again; elasticity is expected from yeast dough, and the dough takes shape again after a short rest. Gather the scraps into a lump, cover them, and let them rest, then make fried dough or small savory bread rolls. For the fried dough, flatten the scraps by hand and score the center with a knife. The only thing to watch is that the dough does not dry out: uncovered scraps form a skin and leave hard pieces inside the dough when kneaded, so cover the scraps while they rest.