The tool you're referring to is commonly known as a static site generator. This technology has gained popularity in web development, with numerous options available and new ones constantly emerging. Many of these generators support markdown, adding to the challenge of selecting the most suitable one for your project.
I first learned about static site generators from an informative blog post titled An Introduction to Static Site Generators by Jessica Smith. The post outlines the advantages of using static generators over dynamic websites and offers a comparison of various tools, with a focus on Jekyll, a prominent choice in this category.
If you're keen on exploring more options, I recommend checking out Node Based Static Site Generators by Alex Johnson. In addition to discussing various generators, the article explores potential Dropbox integration. Some other notable static site generators worth considering include: