A good way to rederive table-driven expression parsing on the spot is to start with recursive descent and notice how it makes a recursive call for every level of precedence, even the levels where "nothing happens" because there's no operator of that precedence level at this place in the input. Use the table to call the "right place in the grammar" directly. This works out to be the precedence-climbing algorithm.

I guess you'd get to the shunting yard from there by turning the remaining recursion into an explicit stack, but I haven't worked that out to check.