You could probably do this at AMS. Incoming passengers mix with outgoing passengers in the corridor from the gate towards the terminal building at the moment. This may change soon but as of now that is how it is. No need to re-clear security as long as they are both H gate flights (or both M gate flights, I suppose), so don't try to do this with a return flight that enters or leaves the Schengen Area.

So get off the incoming flight, go up the stairs, look for the gate of your next flight, and join the queue to board.

Obviously don't check any bags and check in online first!

Ensure you are not booked to come back on the last flight of the day and then if you can't board, go immediately out of the landside (ensure you have a passport/visa combination that can enter the Schengen Area) to the Easyjet ticket desk in Departures 3. Tell them you got to the airport too late and ask them to help, they will very likely charge you GBP60 or equivalent to put you on the next flight as part of Easy's goodwill policy to people who just miss flights.

Please tell us all how funny a look you get from the crew when you get back on (if they recognise you).

At AMS, Easyjet passengers are not told to go to the gate until there is a good chance the aircraft will arrive and they know when it is. So when it is inbound and they know the expected landing time. This is because there is little space and almost no facilities beyond the security check for the H gates pier that Easyjet usually leave from. Further, the ground staff will not check boarding passes and mark passengers as loaded and hold them in the gate holding pen, until the flight is very close, because there are no toilets and only a water vending machine in the holding pen.

My (fairly extensive...) experience of delays to Easy at AMS is that you end up sitting in the main departure lounge watching screens until the delayed flight arrives, then rush the security checkpoint and gate.

There is no conformance at AMS. If you are hand baggage only and you check in online then the first time anyone records your boarding pass is as you are marked as loaded onto the aircraft at the gate.

AMS is fast. The record in my company is 6 minutes to get from the taxi door on the road outside to the aircraft door (HBO, Privium, and a lot of running).

If you really do have free flights to use up, why not day trip it somewhere with 2-3 services per day, instead of a back to back,