A sentence from this site reads ungrammatical.
On the sweet side, don’t pass up the walnut coffee cake, which is served warm, the better to soak up the bourbon-caramel glaze.
Is the better a noun phrase in this sentence? Why is it not better to soak up the bourbon-caramel glaze as an adverbial? Is the sentence grammatical? What grammar function does the phrase the better to soak up the bourbon-caramel glaze serve? Is it a modifier to the main clause?