In this paper, we revisit the problem of Bayesian shape-restricted function estimation. The finite-dimensional Gaussian process (GP) approximation proposed in Maatouk and Bay (2017) is considered, which admits an equivalent formulation of the shape constraints in terms of basis coefficients. This approximation satisfies a wide variety of shape constraints everywhere, whether applied alone, in combination, or sequentially. We propose a new, efficient, and fast algorithm for sampling from a large Gaussian vector extracted from a stationary GP. The proposed approach significantly improves the novel circulant embedding technique proposed in Ray et al (2020) for efficiently sampling from the resulting posterior constrained distribution. The main idea of the algorithm developed in the present paper is to divide the input domain into smaller subdomains and apply a cross-correlated technique to address the correlation structure in the entire domain. As the number of subdomains increases, the computational complexity is drastically reduced. The developed algorithm is accurate and efficient, as demonstrated through comparisons with competing approaches. The performance of the proposed approach has been evaluated within the context of shape-restricted function estimation.