Preheat oven to 425°F.
Use a pastry cutter or two forks to cut the 12 tablespoons of butter and 3 cups of flour together until the mixture resembles coarse cornmeal. While stirring with a fork or a clean hand, add about a tablespoon of water (or milk or buttermilk) at a time, just until the dough holds together. Divide the dough in half and flatten into two round discs. If saving for later, wrap them up and place in the refrigerator.
On a lightly floured surface, roll one of the dough discs out to fit into a 9-10" pie pan and transfer to the pan. The other disc will be used to top the pie later.
In a small bowl, mix together the honey and maple syrup (add the shrub or white wine here, if using, to add a little tang). In a large bowl, toss the green tomatoes with the remaining 4 tablespoons of flour and the salt, and stir in the honey-maple syrup mixture. Transfer the pie filling into the prepared crust. Cut 2-4 tablespoons of butter into small cubes and dot all over the top of pie filling.
Roll out the top crust to fit the pie, and either make a lattice crust or cut air pockets into your solid top crust to resemble a sand dollar. Seal the edges of the two pie crusts with either your fingers or a fork.
Bake for 15 minutes, then reduce heat to 350°F and bake for another 45-50 minutes until the crust is lightly browned. Allow to rest for 10 minutes. Serve at any temperature. Like apple pie in Wisconsin, this pie is also good with a cold slice of cheddar or colby cheese.