1. Make the crust: In a large bowl, whisk to combine the flour, salt, and sugar, mixing well. Add butter and mix gently using a pastry blender, a fork, or your hands, until butter pieces are well coated. Gradually add water, 1 tablespoon at a time, and continue mixing until pea-size crumbs have formed; dough should not be smooth and beaten together like cookie dough.

2. Gather dough together and divide in half. Flatten each half into a disk and wrap with plastic wrap. Transfer dough to refrigerator for at least 1 hour and up to 3 days. Bring to room temperature before using.

3. Preheat oven to 375 degrees with a rack in center of oven. Make the filling: In a large bowl, mix together apples, butter, brown sugar, cornstarch, cinnamon, and salt. Add cheddar and rosemary and stir to combine; set filling aside.

4. On a lightly floured surface, roll out each disk of dough to a 1/4-inch thickness, lightly dusting with flour, as necessary, to prevent sticking. Cut out eight 2 3/4-inch circles and eight 4-by 8 1/2-inch strips, gently rerolling scraps as necessary. With remaining dough, use a fluted pastry cutter to cut out forty 3 1/2-by 1/2-inch strips, gently rerolling scraps as necessary.

5. Press one circle firmly into the bottom of each of eight 1/2-pint widemouth oven-safe glass jars. Line sides of each jar with one 4-by 8-inch strip of dough, pressing it into place, making sure to leave 1/2-inch overhang over the rim of the jar. Spoon filling into jars, leaving about 1/2-inch space from top of jars.

6. Beat remaining egg with 1/2 teaspoon water; set aside. Lay 3 of the remaining 3 1/2-by-1/2-inch strips of dough over one pie horizontally and evenly spaced, leaving the ends overhanging the rim. Starting from the left, take one additional strip and weave it vertically through the horizontal strips in an over-under-over-under pattern, leaving the ends overhanging the rim. Repeat process with a second strip of dough, evenly spaced, to create a lattice top. Use egg mixture to adhere. Repeat entire process with remaining strips and pies. Crimp edges as desired. Brush tops with any remaining egg mixture.

7. Place jars on a baking sheet and transfer to oven; bake until crust is golden brown, about 45 minutes. Serve.