With a whole egg, or three yolks.
Here’s a version from the January 21, 1882 edition of the Goshen (Indiana) Independent:
A Good Mayonnaise Dressing. — Put the yelks of two eggs in a deep dish with a little salt and white pepper; into these stir briskly some olive oil, which must be added very gradually and alternated every little while with a few spoonfuls of vinegar. This dressing should have an agreeable flavor, and a rather stiff consistency. Salad oil should be kept well corked in a dry, cool place, and always in the dark.
From the box of A.D. from Lutz, Florida, by way of Pennsylvania in the 1940s, and originating in Ohio in the 1920s.
1 egg or yolk of three
1 Tbsp. flour
3 cups sugar
Butter size of a walnut.
Moisten with cold water.
Add 1 teacup boiling water and boil until thick.