Place the pineapple flesh in a bowl and puree with a stick blender.
Put a sieve over a clean, heatproof bowl and tip the puree into it. Press with the back of a spoon so that the fine puree passes through but the fibrous parts remain in the sieve.
Stand the bowl of pineapple puree over a pan containing an couple of centimetres (1 inch) of simmering water.
Add the butter and sugar. Stir gently until everything has dissolved together.
Add the room temperature beaten eggs and whisk immediately so that it doesn't scramble.
Continue to heat over the pan, whisking regularly until it has thickened enough to leave a trail if you run your finger over the back of the spoon.
Transfer to a 500ml (17 oz) jar.
It will thicken as it cools and set in the fridge, where you can keep it for up to 2 weeks.