Combine egg and the 1/4 cup milk.
Combine crackers, the 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Dip chicken in egg mixture, then roll in crumbs.
In skillet brown chicken in hot shortening about 15 minutes, turning to brown evenly.
Add the 1 cup milk.
Reduce heat; cover tightly.
Simmer for 35 minutes.
Uncover; cook till tender, 5 to 10 minutes more.
Remove chicken to platter; keep warm.
For gravy, reserve 3 tablespoons drippings in skillet.
In screw-top jar combine 3/4 cup milk, flour, the 1 teaspoon salt, and dash pepper; shake till well blended.
Stir into drippings in skillet.
Blend in 3/4 cup milk.
Cook, stirring constantly, till thickened and bubbly.
Cook 2 to 3 minutes more.
If necessary, thin with a little additional milk