On a flat surface, roll out a large piece of parchment paper, at least 16” long. Using a ruler and a dark marker, like a sharpie, measure out a 14” x 10” rectangle. You may want to use the edge of the parchment box as a guide for your ruler, to be sure it remains straight. Flip the paper so that your dough doesn’t wind up with marker in it. You should still be able to see the markings through the paper.
In a large bowl, add the flour, cream of tartar, baking soda, salt, pepper, lemon zest, and tarragon. Whisk mixture to combine and break up, instead of sifting. Pour into food processor
Remove your butter from the refrigerator and using a sharp knife or bench scraper, cut the butter into small cubes and toss into the food processor immediately. You don’t want to handle it much as it will melt the butter and impact the flakiness of your pastry.
Pulse the mixture to break up the butter and coat the flour. Watch as you’re pulsing to make sure that you wind up with coarse crumbs and no large chunks of butter.
Dump into a large bowl and add the cold buttermilk starting with ½ cup and then adding the rest, as needed, ¼ cup at a time. Combine with your hands, or a spatula and stir to moisten all ingredients the dough should be soft and moist, just holding together. Don’t overmix or press it onto the sides of the bowl.
Generously flour your marked parchment paper and roll your dough out on the center of the rectangle. Using your hands, pat the dough out to fill the rectangle, making sure that it’s evenly distributed throughout.
Spread about half of the room temperature butter on top of the dough with a butter knife or spreader. Then you will fold the dough—using your bench scraper, if you have it, with the help of the parchment paper. You want to fold it as you would a letter, one third on top of the other. Take your new rectangle of dough, rotate it 90 degrees and repeat—patting the dough into the rectangle, covering with remaining room temperature butter and then folding the same way.
Once more you will flatten the dough out to your rectangle. Cover it in plastic wrap and chill in the refrigerator while you finish preparing the filling.
Preheat the oven to 450 degrees.
In a large sauté pan, heat about a tablespoon of olive oil over a medium-high heat and add broccoli and carrots when shimmering. Cook, for about 5-7 minutes, stirring frequently, until they’re crisp tender. When done, they should go into a very large mixing bowl—the largest that you have, as this will be how you combine all ingredients for the filling.
Meanwhile, in the same saucepan used for poaching, add 1 tablespoon olive oil and heat over medium. Add mushrooms, salt, fennel, tarragon, and thyme. Cooking down so that the mushrooms absorb those flavors. About 6-8 minutes.
Add remaining olive oil to the sauté pan used for broccoli and carrots, and heat over medium. Add the zucchini and cook down so that liquid escapes the vegetables and evaporates. About 5 minutes.
Remove the mushrooms from heat and add sherry or madeira to the pan. Lower the heat on the stove and continue cooking. Add cooked zucchini and cook down until the alcohol has evaporated another 3-5 minutes or so.
Add the onions and peas to the broccoli and carrots. Turn off the heat and let the mushroom mixture cool. Cut the chicken breasts into bite-sized pieces, about 1-inch cubes and add to vegetables. Then add the mushrooms and zucchini to bowl.