To prepare the pastry, cut the butter into 1/4-inch cubes and freeze for 5 minutes. 

In a small bowl, whisk together the milk, vinegar and salt. Set aside. 

Sift the flour into a large bowl. Remove the cold butter from the freezer and drop it into the flour mixture. Using a fork, cut the butter into the flour. Stop working the butter into the dough when the butter pieces are about the size of almonds or slightly smaller. Make a well in the center of the bowl and add the milk mixture. Using your hands, mix the flour mixture with the milk mixture until mostly combined. 

Dump the dough out on a floured surface and gently knead, folding and pressing the dough over and on top of itself, working in the milk mixture. The dough will be crumbly. Just keep gathering, folding and pressing. If needed, add up to 1 teaspoon water. Work quickly so the dough stays cold. Fold it over onto itself 9 or 10 times. 

Divide the dough in half and shape each piece into a circular mass. Using a rolling pin, flatten each piece out about 1/2 inch thick, making sure it is in a rounded shape. Wrap each round securely in plastic wrap and refrigerate for at least 1 hour or up to overnight.

To prepare the filling and assemble the tarts, in a large nonstick fry pan over low heat, melt the butter with the olive oil. When just melted, add the shallots and salt and cook, stirring occasionally, until the shallots begin to caramelize, about 30 minutes. Let cool.

Remove 1 ball of pastry from the refrigerator. Have ready a baking sheet, plastic wrap, parchment paper, flour for dusting, a rolling pin and ruler. On a lightly floured work surface, use a rolling pin to "condition" the pastry by beating it down by about 1/4 inch, turning the pastry as you work it. Flour the rolling pin and the top of the pastry to keep them from sticking to each other. Use the rolling pin to start rolling out the dough, turning the dough one-quarter of the way around after a few rolls and continuing to do so until a round pastry takes shape. Keep rolling, adding a light dusting of flour under and on top of the pastry as needed to keep the pastry from sticking. Work quickly; you want it to stay cold! If it's sticking too much, place the pastry on a parchment-lined baking sheet and pop it in the refrigerator for 10 minutes. Roll out the pastry into a 9- to 10-inch round. Weird edges are okay. If there is a tear in the edge, tap your finger into a bit of cold water and seal up the tear. 

Place plastic wrap completely over 1 pastry round, tucking in the plastic wrap around the edges so the dough doesn't dry out in the refrigerator. Place it on a large plate or baking sheet in the refrigerator to rest while rolling out the other pastry in the same manner. Refrigerate both rounds for at least 20 minutes before assembling the tarts.
 
Preheat the oven to 400°F. Line a baking sheet with parchment paper. 

Slice half of the figs into disks and slice the remaining half into quarters.

Place 1 pastry round on the prepared baking sheet. Leaving a 1 1/2- to 2-inch border, spread half of the cheese over the pastry. Top with half of the caramelized shallots. Place half of the fig disks around the edge of the filling, slightly overlapping if needed. Fold the edges over the filling, overlapping the pastry as needed, leaving the center open. Arrange half of the quartered figs in the center of the tart. Cover with plastic wrap and refrigerate for 20 minutes before baking. Assemble and refrigerate the second tart in the same manner.

Brush the edges of the tarts with the egg wash and sprinkle with the sugar. Bake on the parchment-lined baking sheet until the pastry is golden brown, 30 to 35 minutes.

Cut the tarts into wedges and ENJOY!

NOTE: Nicasio Formagella is a locally produced, soft-ripened cheese with a delicate nutty flavor and a creamy texture. Mt Tam, a soft, triple-cream cheese produced by Cowgirl Creamery, is also a great selection. If unavailable, any soft-ripened cheese such as Brie or Camembert would be an appropriate substitute.