烂熟 has a literal cooking sense ("cooked to the point of mushiness") and a figurative sense ("so familiar it's second nature"). The figurative sense often appears in 烂熟于心 (lànshú yú xīn, "committed to memory") and 背得烂熟 ("memorized by heart").
memory
烂 = rotten/falling-apart, 熟 = cooked/familiar. Cooked so thoroughly it falls apart → known so thoroughly it spills out without effort.
