This recipe is from "The Kentucky Receipt Book," by Mary Harris
Frazer, published in 1903:

BANANA PUDDING
Take 1/2 dozen bananas , peel and cut in pieces an inch thick, put in
baking dish and pour over custard made in the following manner:

Custard-One pint (2 cups) of milk, 3 eggs, beat the yolks light, add milk,
also 2 tablespoons of granulated sugar.

Have the milk boiling, add the eggs and let it cook until it thickens;

when cool pour over the bananas.

Meringue
Make a meringue with whites of the eggs and granulated sugar, put on top of custard, set in oven a few minutes to brown.

Serve at once."