My preferred cracker for soup is an oyster cracker recipe by Ivy Manning from the book Crackers & Dips. Paraphrased as follows for two half-sheet pans full:
140 g. AP flour
1 t. kosher salt
1 t. sugar
1 t. baking powder
2 T. cold, unsalted butter
1/3 c. cold water, plus additional as needed
Flour for rolling
Whisk together the flour, salt, sugar and baking powder. Grate the butter into the flour mixture and work it into the flour until it resembles coarse meal. Add water and lightly knead the dough until it comes together in a ball. Cover and rest 15 minutes. Roll the dough onto a well-floured surface to a thickness of 1/8”. Using a sharp knife, cut into squares (or any other shape). Transfer to a parchment-lined baking sheet and spread out as much as possible. Bake at 375 for 14-15 minutes until crackers are showing color on the bottom edges (rotate and turn pans half-way through). Turn off the oven and crack the door about 8”, leaving crackers inside the oven to cool and continue to crisp, at least 30 minutes or until oven cools off. When completely cool, store in an air-tight container.
My notes: Rather than transfer the cut crackers to parchment, I like to roll the dough out on lightly floured silpat to 1/8” and cut into squares with a pizza cutter directly on the silpat. Then I transfer the whole silpat sheet with the crackers to the sheet pan and, without bothering to separate them, bake as per above. I typically have to pull the crackers around the perimeter earlier than the crackers in the center, which take a few minutes longer to bake. Put everything back on the sheet pan (in a jumble is OK) for the final cooling in the oven.