Cut the crusts off the bread and spread one with basil pesto and top with artichokes. Season with salt and pepper.
Top with provolone cheese and the remaining slice of bread. Cut in half.
Crack the eggs into a bowl and add the milk, cayenne pepper and 1 tsp salt. Whisk to combine.
Heat a non-stick frypan on medium heat and add the olive oil and the butter. Heat until butter is sizzling. Dip the sandwich in the egg mixture to thoroughly coat. Fry on one side until golden, about 2 minutes, then carefully flip over and cook the other side for another 2 minutes.