Modulo-Imaging (MI) offers a promising alternative for expanding the dynamic range of images by resetting the signal intensity when it reaches the saturation level. Subsequently, high-dynamic range (HDR) modulo imaging requires a recovery process to obtain the HDR image. MI is a non-convex and ill-posed problem where recent recovery networks suffer in high-noise scenarios. In this work, we formulate the HDR reconstruction task as an optimization problem that incorporates a deep prior and subsequently unrolls it into an optimization-inspired deep neural network. The network employs a lightweight convolutional denoiser for fast inference with minimal computational overhead, effectively recovering intensity values while mitigating noise. Moreover, we introduce the Scaling Equivariance term that facilitates self-supervised fine-tuning, thereby enabling the model to adapt to new modulo images that fall outside the original training distribution. Extensive evaluations demonstrate the superiority of our method compared to state-of-the-art recovery algorithms in terms of performance and quality.