Freely moving solid objects undergoing phase change, such as melting icebergs, falling snowflakes, or dissolving sugar particles, play a key role in many environmental and engineering processes. Simulating these systems is challenging due to the need to couple the fluid dynamics. Particle motion, interface evolution (mass transfer), and heat transfer. While numerous methods have been developed for either moving solids without phase change [1-2] or fixed solids with phase change [3-4], techniques for freely moving solids undergoing phase change remain limited and typically rely on boundary-fitted [5] or classical Lagrangian immersed boundary methods [6], which require time-consuming re-meshing. Therefore, we propose a fully Eulerian framework for the melting/solidification of moving particles that uses a single Eulerian Cartesian mesh and does not require re-meshing. It combines an Eulerian immersed boundary method based on a level-set formulation to track the interface and address fluid-solid interactions. Phase-change induced shape variations are captured by enforcing the Stefan boundary condition at the moving interface using a two-fluid formulation for the temperature equation, i.e., conservation of energy. The approach is validated against benchmark cases and can simulate rigid particles of arbitrary and time-varying shapes; the implementation also allows for different thermal properties (e.g., density, thermal conductivity) between the solid and fluid phases.