Describe the workflow you want to enable

In addition to method="sigmoid" and method="isotonic" it would be great to pass any scikit-learn compatible classifier with a predict_proba to CalibratedClassifierCV.

In particular I would like to be able to pass: method=HistGradientBoostingClassifier(monotonic_cst=[1]) (or #13649) to calibrate a model using a non-parametric method (similar to isotonic regression) but with an adjustable overfitting/underfitting tradeoff by setting max_leaf_nodes and max_iter (which is not possible with isotonic calibration).

Describe your proposed solution

The sklearn.calibration._fit_calibrator private helper would need to accept and clone scikit-learn regressors instead of raising ValueError.

Of course one would need to add new tests + extend at least one of the calibration example to demonstrate this new capability.

Edit: the first version of this issue used HistGradientBoostingRegressor instead of HistGradientBoostingClassifier