Is there a polynomial $f(x,y)$ in two variables, with integer coefficients, such that $f$ is irreducible over the complex numbers (i.e., in $\mathbb{C}[x,y]$), but for every integer $n$, the polynomial in one variable $f(x,n)$ is reducible over $\mathbb{Q}$?

For comparison, there are polynomials in one variable which are irreducible, but reducible mod $n$ for every $n$. See the question Polynomial reducible modulo every integer.

EDIT: As Arnaud Mortier's example showed, I should have said reducible over the rationals, not the integers, so I edited the question.