Does так push the meaning closer to 'My older sister is SUCH a good cook' rather than simply stating that she is a good cook?
Actually, I think this can only mean that she cooks well, not that she is a good cook. I think так goes with verbs, like "to cook" and такая/такой/такое go with nouns, like "a cook".
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Because "good" is an adjective and adjectives modify nouns only. The verb "cook" is the word being described and adverbs describes verbs. "Well" is the adverb form of "good".