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The formation of the stellar mass within galaxy cluster cores is a poorly understood process. It features the complicated physics of cooling flows, active galactic nucleus feedback, star formation, and more. Here we study the growth of the stellar mass in the vicinity of the brightest cluster galaxy (BCG) in a z = 1.7 cluster, SpARCS1049+56. We synthesize a reanalysis of existing Hubble Space Telescope imaging, a previously published measurement of the star formation rate, and the results of new radio molecular gas spectroscopy. These analyses represent the past, present, and future star formation, respectively, within this system. We show that a large amount of stellar massâ€"between (2.2 ± 0.5) Ă— 1010 M ⊙ and (6.6 ± 1.2) Ă— 1010 M ⊙ depending on the data processingâ€"exists in a long and clumpy tail-like structure that lies roughly 12 kpc off the BCG. Spatially coincident with this stellar mass is a similarly massive reservoir ((1.0 ± 0.7) Ă— 1011 M ⊙) of molecular gas that we suggest is the fuel for the immense star formation rate of 860 ± 130 M ⊙ yrâˆ'1, as measured by infrared observations. Hlavacek-Larrondo et al. surmised that massive, runaway cooling of the hot intracluster X-ray gas was feeding this star formation, a process that had not been observed before at high redshift. We conclude, based on the amount of fuel and current stars, that this event may be rare in the lifetime of a cluster, producing roughly 15%â€"21% of the intracluster light mass in one go, though perhaps a common event for all galaxy clusters. [ABSTRACT FROM AUTHOR]