Sift the flour and salt into a medium bowl. Add 6 tablespoons of the cold butter and mix with a pastry blender or your fingers until the mixture resembles coarse crumbs. Add the water 1 tablespoon at a time and mix until the dough comes together and is no longer dry, being careful not to overmix. Form into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes.

Roll out the dough on a lightly floured surface to 10-inches in diameter. Transfer to a tart pan with a removable bottom and place in the refrigerator to rest for at least 20 minutes.

Preheat the oven to 400 degrees F.

Line the pastry with parchment paper and fill with pie weights or dried beans. Bake until the crust is set, about 12 minutes. Remove the paper and weights and bake until golden brown, about 8 minutes. Remove from the oven.

In a skillet, melt the remaining tablespoon of butter over medium-high heat. Add the ham and cook until beginning to color and the fat is rendered, about 3 minutes. Add the shallots and cook for 1 minute. Remove from the heat and spoon into the bottom of the tart.

In a bowl, beat together the eggs and egg yolks. Add the cream and beat well. Add the mixed herbs, thyme, salt, and pepper, and mix well. Pour into the tart shell and bake until the top is golden and the filling is set, about 25 minutes. Remove from the oven and cool on a wire rack for 20 minutes before serving.