In a medium bowl, combine cake flour, instant yeast, baking soda, cream of tartar, and sugar. Whisk together until fully blended.
In a small saucepan, gently heat the butter, vegetable oil, and water, allowing the butter to melt completely. Cool this mixture to around 120°F, ensuring it is warm to the touch but not too hot.
Create a well in the dry ingredients and pour in the warm butter mixture. Using an electric mixer, blend on medium speed at first, then increase to high. Continue mixing until the dough begins to form, and all ingredients are well incorporated.
Transfer the dough to a lightly floured surface and knead it by hand until it forms a soft, smooth ball. If the dough feels sticky, gradually add more flour in small amounts. Conversely, if it feels too dry, incorporate a little water as needed to achieve a soft, pliable dough.
Lightly grease the mixing bowl, place the dough inside, and cover it with plastic wrap. Refrigerate the dough for a minimum of 12 hours, and up to 18 hours for the best results.
Once the dough is ready to use, take it out of the refrigerator and let it rest at room temperature for about 15 minutes.
Preheat your oven to 400°F. Line a large baking sheet with parchment paper or lightly grease it.
Knead the rested dough for a few minutes to make it smooth and easy to work with. Divide the dough into four portions, rolling out each piece as thin as possible—using a pasta roller is ideal for achieving a delicate, crispy cracker.
Using a pizza cutter or pasta wheel, slice the dough into 2x2-inch squares. Arrange the squares closely together on the prepared baking sheet, as they will slightly shrink while baking. Repeat this process for all portions of dough.
Prick each cracker with a fork to create the classic perforated pattern. Lightly brush the tops with water and sprinkle with sea salt or herb salts.
Bake the crackers for 8 to 10 minutes, watching closely around the 8-minute mark to prevent excessive browning, unless you prefer an extra-crispy texture.
Once baked, remove from the oven and let the crackers cool directly on the baking sheet.
Store the cooled crackers in an airtight container for up to a week, assuming they aren't devoured sooner!