Cut the cauliflower into medium chunks that will fit in the tube of a food processor.
Fit the food processor with a grating disc and grate the cauliflower by pushing it through the tube. Alternatively, cut the half head of cauliflower in half and grate with a box grater or mince as finely as you can by hand.
Pat the cauliflower dry to remove excess moisture.
Heat the oil in a large skillet on medium-high. Work in batches if you have a smaller pan so the ingredients don't get overcrowded and steam.
Add the cauliflower and stir to coat in the oil. Let it cook for 2 minutes.
Add the edamame and stir well. Cook for an additional 4-5 minutes until lightly browned.
Stir in the ponzu sauce and cook for an additional minute.
Remove the pan from the heat and stir in the salt. Taste and adjust for salt if desired.