What is the best way to get a close-to-fair coin toss from identical biased coins?
Tossing n biased coins and taking the parity of heads gets exponentially close to $\frac{1}{2}$. 

[For a proof, consider a random variable that is -1 when heads and 1 when tails, then
the probability that there are an odd number of heads is just the $E\left[\frac{1}{2} + \frac{1}{2}\prod_i X_i\right] = \frac{1}{2} + \frac{1}{2}\delta^n$]

Perhaps this is also optimal for the following reason. Let $f$ be any composition function of these bits. Then, the $\text{Bias}(f) = \sum_S \hat{f}(S) \delta^{|S|}$ and the best $f$ seems to be the parity function (isn't it?). 

If you are interested in composition functions of lower complexity, then perhaps a paper of Ryan O'Donnell on `Hardness amplification within NP' would be very relevant. There he uses monotone composition functions for hardness amplifications and the functions that work are characterized by their noise sensitivity.