  Let $f$ be a Hochschild $2$-cocycle and let $A_f$ be an infinitesimal
deformation of an associative finite dimensional algebra $A$ over an
algebraically closed field $\Bbbk$. We investigate the algebra structure of the
Ext-algebra of $A_f$ and, under some conditions on $f$, we describe it in terms
of the Ext-algebra of $A$. We achieve this description by getting an explicit
construction of minimal projective resolutions in $\mod A_f$.
