Start by making the mayonnaise. Add the egg yolks, lemon juice, vinegar, dry mustard, salt, sugar, and cayenne to the food processor. Pulse a few times to combine.
Slowly, and I mean super slowly, drizzle the olive oil through the funnel with the food processor running. Once all of the oil has been incorporated, you have mayo! Totally easy.
To make the pimento cheese, add one cup of mayo to a large bowl. Add sage, lemon juice, dry mustard, cayenne, Worchestershire sauce and mix to combine. Add drained pimento and shredded cheese. Season with salt, pepper, and hot sauce, to taste. Mix to combine. Serve with crackers.