  We propose an adaptive and provably accurate tensor completion approach based
on combining matrix completion techniques (see, e.g., arXiv:0805.4471,
arXiv:1407.3619, arXiv:1306.2979) for a small number of slices with a modified
noise robust version of Jennrich's algorithm. In the simplest case, this leads
to a sampling strategy that more densely samples two outer slices (the bread),
and then more sparsely samples additional inner slices (the bbq-braised tofu)
for the final completion. Under mild assumptions on the factor matrices, the
proposed algorithm completes an $n \times n \times n$ tensor with CP-rank $r$
with high probability while using at most $\mathcal{O}(nr\log^2 r)$ adaptively
chosen samples. Empirical experiments further verify that the proposed approach
works well in practice, including as a low-rank approximation method in the
presence of additive noise.
