Combine flour and salt in a medium mixing bowl; cut in shortening with a pastry blender until mixture resembles coarse meal. Sprinkle 5 to 6 tablespoons water evenly over surface of flour mixture; stir with a fork until dry ingredients are moistened, shape dough into a ball; chill.
Drain cherries, reserving liquid; chop cherries. Combine cherries, reserved liquid, pecans, jelly, cinnamon, and Cognac in a medium mixing bowl; mix until thoroughly blended. Set aside.
Roll half of pastry to 1/8-inch thickness on a lightly floured surface; cut with a 3-inch round cutter. Place a heaping teaspoon of reserved cherry mixture in center of each cookie; overlap sides, forming a cylinder Insert a cherry half in each open end. Place 2 inches apart on lightly greased cookie sheets. Repeat procedure with remaining dough. Bake at 400° for 20 to 25 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.
Combine sugar, 1 cup water, honey, and lemon juice in a saucepan; bring to a boil. Reduce heat; simmer, uncovered, 15 minutes, stirring occasionally. Cool glaze to room temperature; drizzle over cookies. Let dry completely before serving.