Minimal pairs are those vowels which are so similar that it's hard for a language learner to pronounce them differently. The classic example is sheep and ship or sheet and....
The traditional way to practice is to read long lists of pairs, paying attention to pronunciation, for example: bit - beat, pill - peal, it - eat, etc. However, I find this way too easy! Of course you can pronounce the words correctly when concentrating on nothing but the two vowels, alone. The challenge arises with vocabulary used in sentences.
So far I've found one sentence exercise online practicing the difficult SILVER PIN and GREEN TEA pair. It's posted by Teacher John on YouTube.
Then there is the famous poem "The Chaos" by Gerard Nolst Trenité. Although quite long and comprehensive, it is a bit too complicted for effective pattern practice.
So of course I am writing my own couplets.
Green Grendel grins and grits his teeth. He greets the tree and hides beneath.
Minnie the meany just missed with her mit when Pete pitched the peach or maybe the pit.
Yep, it needs work.