Sauté sausage slices for approximately 3 minutes to lightly brown in a large pot.
Set aside, leaving drippings in pot.
Bring 2 quarts of water, the potatoes, onion, garlic, and salt to a boiling same pot, simmer until the potatoes are tender, about 15 minutes.
While that is cooking, wash the greens and remove the center stems. Stack the greens, rollup like a cigar, and slice as thinly as possible; setting aside.
Remove the potatoes, onions, and garlic from the boiling liquid and place into a blender or food processor, adding a little pot liquid to help form a puree. After blending, return the potato puree to the pot.
Add the olive oil and the greens to pot. Return contents of pot (broth, greens, etc) to a boil, reduce the heat, and simmer uncovered for only 5 minutes so as to maintain the bright green color.
Either add slices of previously browned sausage into the pot prior to serving or wait to place on top of soup after served into bowls.