Heat the oven to 350. Put half the walnuts in a food processor and pulse until finely ground. Place them in a large bowl with the rest of the almonds, the flours, sugar, baking powder, baking soda, lavender, and salt and mix well. Add the honey and ¾ cup water and mix until just incorporated. Add a little extra water if needed to bring the dough together.
Lightly grease two baking sheets with a little oil and dust with flour (I just use parchment paper and only one baking sheet). Divide the dough in half and shape each half into a 2-inch wide log. Put each log on a baking sheet and bake until golden and beginning to crack on top, 30 to 40 minutes. Cool the logs on the sheet for a few minutes. Lower the oven temp to 250.
When the loaves are cool enough to handle use a serrated knife to cut on a diagonal into ½-inch slices. Place the slices on the sheets, return to the oven and leave them there, turning once, until they dry out some, about 25 to 30 minutes. Cool completely on wire racks.