Use ITA Matrix to find your itinerary.
Departing from: JFK
Destination CEB
Click Advanced routing codes
In the advanced routing codes field, enter "icn / minconnect 700" without quotes, where 700 is the minimum connection time you want, in minutes. "icn" forces a single connection at ICN.
You may want to sort by duration. When you find the itinerary you want to book, click on the price on the left to get the full detail page. You can't book on ITA Matrix, but keep this page open.
Open a new tab and go to bookwithmatrix.com. Copy the text of the full detail page in ITA Matrix (Windows: Ctrl + A then Ctrl + C, Mac: Command A then Command C). Paste into the search box on bookwithmatrix.com. Bookwithmatrix will give you links to booking sites with the itinerary populated and ready to book.