Compositional MRI (cMRI) offers sensitivity to biochemical changes that can precede morphological changes in tissues and offer quantitative assessments of musculoskeletal tissue health but suffer from long scan times. We present a recurrent encoder-decoder architecture that predicts ground truth T2 maps from spatially undersampled echo images. Reconstructed maps showed strong fidelity to ground truth in lumbar spine IVDs and knee and hip knee cartilage. Reconstruction errors were below clinically significant T2 changes through R=12 in the knee and lumbar spine and R=8 in the hip. This work marks progress towards a clinical pipeline that reduces cMRI acquisition time.