Does this HP LaserJet 500 colorMFP M570dn have a double sided scanning feature

Yes it does have a double sided scanning feature. Here is also a guide on how to do it
Copy on both sides (duplex) Copy on both sides automatically

1. Load the original documents into the document feeder with the first page facing up, and with the top of the page leading.
2. Adjust the paper guides to fit the size of the document.
3. From the Home screen on the product control panel, touch the Copy button.
4. Touch the Settings button.
5. Scroll to and touch the Two-Sided button.
6. Touch the arrow buttons to scroll through the options, and then touch an option to select it.
7. Touch the Black or Color button to start copying.

Copy on both sides manually

1. Place the document face-down on the scanner glass with the upper-left corner of the page in the upper-left corner of the glass. Close the scanner.
2. From the Home screen on the product control panel, touch the Copy button.
3. Touch the Settings button.
4. Scroll to and touch the Two-Sided button.
5. Touch the arrow buttons to scroll through the options, and then touch an option to select it.
6. Touch the Black or Color button to start copying.
7. The product prompts you to load the next original document. Place it on the glass, and then touch the OK button.
8. Repeat this process until you have scanned the last page. Touch the Done button to finish printing the copies.