in [@Rump8] completed the classification of braces with a cyclic additive group; these so-called cyclic braces [@Rump2] are equivalent to the T-structures of Etingof et al. [@ESS].

Recall that the multiplicative group $(B,\cdot )$ of any finite left brace $(B,+,\cdot )$ is solvable (see [@ESS Theorem 2.15] and also [@Rump page 167]). One of the natural questions that arose in this context is to determine the orders of finite simple left braces. In particular in [@BCJO] (Problem 5.2) the following problem is stated: for a given pair of different primes $p$ and $q$, determine exponents $n$ and $m$ for which there exists a simple left brace of order $p^nq^m$. A breakthrough came from the recent result of Bachiller, providing the first nontrivial example of a finite simple left brace [@B3]. In [@BCJO] and [@BCJO2], Bachiller and the authors have made progress on constructing several classes of finite simple left braces, this via the matched products and asymmetric products of braces.

The main aim of this paper is to prove the following surprising theorem that shows that there is an abundance of finite simple left braces, even when the multiplicative group is metabelian and all its Sylow subgroups are abelian (the 