For $n\geq 2r$, let $G_{r,n}$ be the Grassmannian of $r$-dimensional subspaces in $\mathbb F^n$, where $\mathbb F$ is a real division algebra. We construct a family of invariant differential operators on $G_{r,n}$ whose spectrum is certain specializations of Okounkov's interpolation polynomials of BC type. These operators, which we call them quadratic Capelli operators, are obtained by lifting a natural basis of the algebra of invariant differential operators on the symmetric space of $r\times r$ Hermitian matrices over $\mathbb F$, known as the Capelli basis. This is a joint work with Siddhartha Sahi.