Hi there,
I want to dig in a little about what's concerning you here. Are you worried that you're splitting link equity? Because, it's okay to have 4 pages about chocolate cakes. There's no penalty from Google for having multiple pages about the same thing - just think about how many pages Nordstrom has for black sweaters. There's actually a benefit to having multiple pages on the same topic, if you're willing to write unique content for each page. It means you can rank for more long tail keywords, just as you mentioned your .html pages do, since each page will have a slightly different angle.
So, if your question was about duplicate content, know that you're okay.
Leave the URLs as they are, but tweak the page titles and headers so they more clearly target the long tail search term that they're ranking for. Link to the .html versions of /chocolate-cake from /chocolate-cake.asp so that's clearly the higher level page, and spend more time optimizing that.
If, on the other hand, what you're worried about is link equity, the idea that by having 4 pages about chocolate cakes (and 4 pages for every other other baked good), you're getting 25% of your link potential going to each page, making 4 PA 20 pages when you could have 1 PA 30 page, then there are a few things to look at.
If there are external links to all 4 pages, then your answer lies in your competition. Search for the primary keyword that you'd hope you'd rank for if you could combine link equity for all 4 pages with the Moz toolbar turned on. Look at your competition - would you be able to beat that? Does your DA compete with other pages? Would your potential link count, once you had links from all 4 similar pages, allow you to rank on the first SERP?
If you have no chance of ranking for your primary keyword, I suggest that you stick with your 4 variations and make sure you rank for a wide variety of terms around your core keyword. That'll get you more traffic, in the end.
If you could rank on the first page for your primary keyword once you redirected those links from the .htmls, try to consolidate the content from all 4 pages. If you're cautious like me, I would do it one page at a time, combining content from both pages, redirecting one page, and then making sure that the .asp page can rank for the long tail terms that the .html page I redirected was ranking for before moving on. If you're less cautious, you can do them all at once, but you may lose that long tail traffic.
Wow, that was a lot of "if"s! I hope I didn't lose you there. Also, I hope I answered the question you were getting at.
Let me know!
Kristina