Thoroughly combine whole-wheat flour, all-purpose flour, chopped rosemary, baking powder, salt and pepper in a large bowl. Pour buttermilk over the flour mixture and quickly stir it in. Pour a few tablespoons warm water over the flour, stirring it in as you go. Repeat, adding more water a few tablespoons at a time, until the dough comes together to form a soft ball. (You want the dough to be very soft, close to being slightly sticky, so if you add an extra tablespoon or so, it won’t hurt it.) Using your hand, gather the ball, picking up any dry flour in the bottom of the bowl, and knead it in the bowl for a minute or two to form a smooth, soft ball of dough. (If it’s a little too sticky to handle, dust your hand with flour, but do not add any more flour to the dough if possible.) Cut the dough into 4 equal portions. Lightly coat a large plate with cooking spray. Shape each portion of dough into a round the size of a hamburger bun and put it on the plate. Coat the tops with cooking spray (or brush with oil), cover with plastic wrap or a slightly dampened cloth, and let sit at room temperature for about 30 minutes. Place a pizza stone or large cast-iron skillet on the lowest oven rack; preheat to the highest bake setting (500-550°F). To prepare spread: While the dough rests, heat oil in a small skillet over medium-high heat. Add yellow split peas and toast until golden brown, 2 to 4 minutes. Transfer the peas and any remaining oil to a blender. Add 1/3 cup water, lemon (or lime) juice, tomato, garlic, rosemary, salt and pepper and puree, scraping down the sides as needed, to make a slightly gritty puree. Lightly flour a small work area. Press a piece of dough down to form a patty. Roll out or pat the dough into a round roughly 6 to 8 inches in diameter, dusting with flour as needed. Make sure the round is evenly thin, with no tears on the surface. Place the round onto the hot pizza stone (or skillet). Within seconds, it will start to bubble in spots. Close the oven door and cook until golden brown on the bottom and light brown patches appear on the top, 3 to 6 minutes. Remove and slide the flatbread between two pieces of foil to keep warm. Repeat with the remaining dough rounds, stacking them in the foil to keep warm. Serve the spread alongside the flatbreads.