For one offs, you may want to look into heat transfers.
There are many different types. Ones that feel like felt are called flock, and they are solid colored pieces of material that is cut into the shape of your design with a vinyl cutter.
You can read more about the different printing methods here:
Pros and Cons of Each T-Shirt Printing Method
and here:
What is the Quality of Different T-Shirt Printing Methods? A list in general order.
As you read through those threads, you'll probably have more questions

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