For the crust:
Place flour, rosemary, sugar and salt in a large mixing bowl and stir well to combine. Add the butter and using a pastry blender, fork or fingers, gently work into the flour mixture until butter is the size of peas. Add the water, one tablespoon at a time, and stir with a spatula until the dough comes together into a ball. Turn out dough onto plastic wrap and divide in two. Gently press out both halves into round disks. Wrap dough tightly and place in the refrigerator to chill for at least 1 hour.
For the pie:
Preheat oven to 350°F.
Roll out one of the disks of chilled pie dough into a large circle with about 1/8-inch thickness, and gently lay dough into a pie dish. Cut off excess dough, and crimp edges decoratively. Place the pie dish in the freezer for 30 minutes.
Meanwhile, place the figs and pears on a foil-lined baking sheet. Drizzle the fruit with the honey. Place the baking sheet in the preheated oven and roast for 25 minutes to release some of the juices. Remove from the oven and set aside to cool. Once the fruit is cool to the touch, use a slotted spoon to transfer just the fig and pear pieces to a large mixing bowl and discard any juices on the baking sheet.
Place an empty baking sheet into the oven to preheat.
Add the sugar, fig jam, flour, lemon juice, cinnamon, nutmeg and salt to the bowl with the figs and pears. Gently stir to combine and set aside.
Roll out the second disk of pie dough to about 1/8-inch thickness. Cut the dough into 1-inch wide strips.
Remove the pie dish from the freezer. Gently stir the figs and pears again to combine, then pour the fruit into the pie crust, discarding any accumulated juices in the bottom of the bowl. Working quickly, top the fruit with the pie crust strips arranging in a lattice pattern, tucking the edges into the crust. Lightly brush the lattice strips and pie crust edges with the beaten egg.
Place pie dish in the oven on the preheated baking sheet. Bake until the filling is bubbling and set in the middle, and the crust is golden brown, about 40-50 minutes. Loosely cover pie with foil if the top crust browns too quickly. Remove pie from the oven and allow to cool completely before cutting, about 2-3 hours.