Learn Finnish: Mitä enemmän urheilen, sitä enemmän jaksan mökkeillä. - The more I exercise, the more energy I have to spend time at a cottage.

Finnish uses the partitive forms of mikä (what) and se (it). The first half starts with mitä and the second half starts with sitä, both followed by a comparative adjective or adverb. So mitä enemmän..., sitä enemmän... literally means "what more..., that more...".

Since our current lesson focuses on mieluummin and kuin, could we use them to express this idea?

No, because this sentence isn't about preferring one thing over another. The structure mieluummin X kuin Y means "I would rather do X than Y." Here, you are expressing a proportional relationship ("the more X, the more Y") using the mitä... sitä... structure, which pairs two comparative adverbs like enemmän together.

Is mökkeillä a standard verb, or is it slang?

It is a standard, very common verb! Finnish frequently creates verbs from nouns using suffixes like -illa or -eillä. By taking the noun mökki (cottage) and adding the suffix, you get mökkeillä, which efficiently means "to spend time at a cottage."

Why does mökkeillä stay in its basic dictionary form here?