I have seen this result in several places without an English reference:

There exist infinitely many primes $p$ such that $p-1=2q_1q_2$ where $q_1$ and $q_2$ are prime numbers with $q_1,q_2>p^{1/4}$.

There is a French reference (E. Bombieri. Le Grand Crible dans la Theorie Analytique des Nombres. Asterisque 18 Societe Mathematique de France 1974). However, I have not been able to find. I am wondering if someone knows an English reference for this claim or knows of similar results about small number of divisors of $p-1$.

**Update:** the french reference produced in the answer does not include this statement. I expected the result to appear there as stated by Murty in this article on page 14 he mentions this statement (with $1/4$ replaced by $\theta>1/4$) and asks the reader to consult the mentioned reference for 'technical details'.