Why caramel crystallize after adding butter

Quite simply, it's the fat content.

Whole milk or "full-fat" milk is 3.25% fat by weight. Heavy cream is 36-40% fat by weight. These two products are at opposite ends of the fat spectrum, and there's very little difference between 1% and 3% when it comes to an item such as caramel sauce, for which the optimal ratio is about 50% fat. (A little butter can boost the fat content from 40% to 50%).

You might be able to substitute standard/single cream (18-20%) or maybe even coffee cream/half-and-half (10%), but any lower than that and you're just making sugary milk.

Other alternatives to (possibly) get it thicker:

• Use (much) less milk; I'd advise not attempting a direct substitution, just find a recipe based on milk. Even the best milk-based caramel sauce will still be substantially runnier and/or grittier than a cream-based sauce.

• Considering that butter is 80% fat and homo milk is 3.25%, you could use a mixture of (approximately) half milk and half butter that would emulate the fat content of heavy cream. I've never tried this personally, and I suspect that the flavour might be a little off, but at least it would be closer to the expected texture.

• Try a reduction (simmer off the water in the milk). You'll be simmering a long time, and you'll have to watch it very carefully to make sure it doesn't burn, and you'll probably have a nasty stuck-on mess to clean up in the pan afterward, but it will thicken.

You don't tell us neither the ratio of double cream to caramel, nor the time you heat the completed mix, so this is just a guess. But it sounds logical that your problem is evaporation.

Double cream consists mainly of fat and water. I don't remember the exact percentages, but more than half of it is water. So, if you heat cream, part of it evaporates during the heating, and it continues evaporating after being added to the pan with bubbling caramel. But if you use cold cream, its water hasn't evaporated during a heating phase, and if you add a large amount of cream to a hot caramel mixture, the whole mixture cools considerably. If you don't heat it and let it simmer for long enough afterwards, the water content of the cream continues thinning the spread. You end up with a runny sauce instead of a sticky spread.

Instead of pre-boiling, you should be able to just simmer for longer time after adding the cream, if you find it more convenient. But you'll have to try it a few times until you have found the cooking time which gives you optimal consistency.