I stopped with the Daily UI due of it not giving any kind of benefits aside from just the aesthetic part. However one way I go about it is always sketch out notes or insights in my notebook. For example that one you quoted, initially started of me looking at our own local website and recalling what F-I was doing, which is "What If" project.
So I went about asking myself what I would do differently when it comes to movie sites etc. which made me come to that design. This all started on paper (always do).
But some interesting things you can do is look at your local websites, and see what you would do differently and whatnot, like go through the process of asking questions to yourself. This works best for local sites you already know about.
As for the current designs that I am doing, I simply save a lot of things that inspires me. Especially minimalism type of work or the other thing I do is shape exploration, and the ones that looks interesting to me, I turn into the designs you see me doing on a daily basis.
Hopefully this answers your question. Probably went off the tangent a bit.