First of all, prepare the béchamel sauce: melt the butter in a saucepan with a thick bottom, then stir in the flour all together.
Also add the milk (even better if previously heated) mixing well with a whisk, then place on the heat over low heat and cook until it has thickened, continuing to stir constantly.
Remove from the heat, season with salt and pepper and add the gorgonzola, stirring until it melts completely.
Transfer to a plate, cover with cling film and leave to cool completely.
In the meantime, peel the pear, remove the core and cut into cubes.
Then cook for 5-10 minutes (they should soften) in a non-stick pan with sugar, vinegar and a drizzle of oil, stirring occasionally.
Cut the gorgonzola into small pieces.
When the béchamel is completely cold, turn it out onto a lightly floured work surface, sprinkle with more flour and divide into about 10 pieces with a floured knife.
Take one piece at a time, place a few cubes of pear and a piece of cheese in the center and close well, creating a ball.
Proceed with the breading: beat the egg on a plate, dip the balls first in the egg and then in the breadcrumbs.
Proceed with a second breading step: dip the already breaded croquettes again in the egg and then again in the breadcrumbs.
Finally, fry in already hot oil, a few at a time, draining them on kitchen paper once they are golden brown.
The gorgonzola and pear croquettes are ready, serve them nice and hot.