Numerical simulation of moving interface problems often requires the solution of elliptic PDEs involving coefficients that can be discontinuous and sources that are singular. Since the interface is moving, it is advantageous to solve the problem on a fixed Eulerian grid which does not conform to the interface as it moves. We propose an intuitive new method which acheives second order accurate results in L-infinity on a fixed cartesian grid with embedded interfaces. The method is largely independent of the geometry and the interface can be represented either as an arbitrary (closed) segmented curve or a levelset. The problem is formulated as a variational constrained minimization problem which preserves a symmetric positive definite discretization.