In Painter's Help Topics you can find instructions, but I'll add a few things you probably won't find there.
What you want, in Corel Painter, is to create a Captured Dab brush variant. That means the image on which the brush dab is based needs to be captured (selected) and saved as the Captured Dab JPG file associated with the Captured Dab .XML brush variant file.
Make the image large enough so if you increase the brush size when painting, you'll still have a nice stroke. The image will need to be similar to the one you show in your post above, in that it will need to have some white background around the shape you want to use. Painter will save it automatically as a JPG file and the white background will be masked so the image won't be square-ish, only the shape you wanted. The JPG Captured Dab image file stored with your .XML Captured Dab brush variant file will be a negative of the image you selected and captured and both files will have the same name, whatever you named your custom brush variant.
To create a Captured Dab custom brush variant:
1. Choose an existing brush variant that's close to the brush variant you want to create (of course the settings can be adjusted later so it doesn't have to be exact).
2. Save that brush variant as a custom brush variant with a unique name not already used by Painter.
3. Create any image you want to use for the Captured Dab image.
NOTE: In the following step, don't hold down the Shift key to make the selection square because if you inadvertently hold down the Shift key then click and drag, Painter will think you want to add to an existing selection and in Step 5, the Capture Dab command won't be available.
4. Using the Rectangular Selection tool, drag a square-ish selection around the image.
5. With your just-saved custom brush variant selected, in the Brush Selector menu, choose Capture Dab.
6. Save the custom brush variant again with the same name.
7. Make any other brush control adjustments you want to get the desired result.
8. Again, save the custom brush variant with the same name so you won't lose any of the brush control adjustments.
It takes longer to type this than it does to make a Captured Dab variant and once you've done it a couple of times, it'll be second nature and you can have a whole collection of Captured Dab variants to play with.