Whisk the white wine vinegar and sugar until the sugar is mostly dissolved (it's okay if there is still some undissolved sugar). Peel the shallot and grate it on a microplane or the smallest holes on a box grater directly into the bowl. Add the poppy seeds, salt, and ground mustard, and whisk to combine.
Whisking the dressing steadily, pour the oils into the dressing in a slow stream. Continue whisking until completely combined.
Transfer to a covered container and store in the fridge for several weeks. The dressing will separate as it sits; shake to recombine before using.