I never heard of shallow parsing, but I have a theory that sort of does it. I don't often see a question that seems to license me talking about it.
Consider a variant of context free grammar in which I. heads are not assigned to grammatical types (N, A, V, P, ...) but are rather introduced directly by phrase structure rules (S1 -> NP1 loves NP2), and II. grammatical types are distinguished by their degree of embedding, which I note with a digit suffix (0, 1, 2, 3). My preceding illustration means that a finite clause (S1) consists of a nominative NP (NP1) followed by pronunciation "loves" followed by an accusative NP (NP2).
The sense in which this gives a shallow parsing is that much of the embeddedness which requires huge tall trees in conventional syntactic theory is there in the psr. Much of the apparent branching structure accompanies lexical forms of verbs (which are psrs). I assign intrinsic embeddededness levels to the various auxiliaries of English and the various adverb types (Adv0 is performative, Adv1 is sentential, Adv2 is manner, Adv3 is degree).
You can make tall trees if you want, though. Corresponding to the principle of the transformational cycle, psrs are expanded always starting with the most embedded parts.
So if you think of parsing as associating psrs with strings of words and trees, there are many fewer associations required for a tree of a given depth, so the parse is shallow in that sense.