The first recipe I found had a whole bunch of vegetable shortening as the first ingredient. Okay, I'm not terrified by shortening, but I figured I could do better. The second recipe had so much sugar that it sounded more like a cookie than a cracker. I was hoping to find something a little less sweet than regular graham crackers, not more sweet.
The third recipe looked like a perfect graham cracker. If you were feeding prisoners in solitary confinement.
Rather than search for recipes that might not exist, I decided to wing it. About all I used from the recipes was that proportion of 1 teaspoon of baking soda to three cups of flour. This may not be the absolutely final version of this recipe, but it's it's awfully close to what I was looking for.
1 teaspoon baking powder
1 teaspoon kosher salt
2 teaspoons vanilla
3 cups whole wheat flour
1/2 cup water
In the bowl of a stand mixer, cream the butter, sugar and honey until it's light. Scrape down the bowl as needed. With the mixer running, add the salt, baking powder, and vanilla, beating until it is well incorporated.
Add the flour one cup at a time, alternating with the water, beginning and ending with the flour. Beat until well combined and it can form a cohesive ball.
Divide the dough into 3 pieces. On a lightly floured surface, roll the first piece to a rectangle of about 10x12 inches. Move the dough to the parchment-lined cookie sheet. If it's easier, you can roll on the parchment directly.