Hi Amy :-) Here is a recipe that I found on the internet that seem to fit your specifications. I have not tried this recipe.

Communion Bread Recipe

A careful study of the scriptures relating to the feast of the Passover, which was sacredly observed by God's people in days of old, together with those which speak of the institution of the Lord's Supper, shows conclusively that the bread used was of the unleavened kind. The grain used in the making of the flour, moreover, so far as is known, was ground entire, the white beads now in common use being but a modern invention.

In the strict sense of the word, white bread is not a true symbol of the body of the Lord. He is the great Life-giver; but white bread, if depended upon exclusively for food, leads to disease and premature death. In the times of old, special directions were given as to what should enter into the making of bread for sacramental purposes - "fine flour" "mingled with . . . beaten oil." (Exodus 29;40; Leviticus 2:1.) In the making of the following bread, it is necessary that the flour be ground fine; and if the directions are followed, the bread will be tender, and of a good flavor.

Communion Bread

2 cups entire wheat flour (ground fine)
1/2 teaspoon salt
6 tablespoons of purest vegetable oil
9 tablespoons cold water

Add the salt to the oil in a round bowl, and pour in the water in a very slow stream, beating constantly with a silver fork until thick and white ( a temporary emulsion). Pour onto the flour all at once, and mix lightly into a dough. Turn out on a floured board and knead, folding it over and over to inclose air, and pounding it with a wooden mallet ( a wooden potato masher is excellent) until quite elastic, which takes about 5 or 6 minutes. Roll out to the thickness of pie crust, mark with a dull knife into 3/4-inch squares, lay in a baking pan, and bake in a medium slow oven. Avoid browning it, except a slight tinge, as browning gives it a strong flavor.