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It seems that BlueApron blog is using a custom design for WordPress. If you would like to achieve this functionality, it requires a heavy modification in the code as it is currently not possible with Sparkling because Sparkling is not designed to provide that look.
But since Sparkling uses full content display options by default. the_content if you are familiar with WordPress functions.
Which means that you can use read more functionality which is built in WordPress. That way you will have to do it manually but it can be done fairly easily with no coding required.
Thank you so much! That was so helpful! I have done what you have recommended with the “Read More” function. I have created two temporary posts for this and have set them to “sticky” to stay on the home page. I would like to know if you can suggest a method to push these sticky posts to the bottom of the page rather than the top?