Trim sugar snap and snow peas, then blanch along with shelled fresh peas.
Rinse leek well, flipping layers under running water to remove grit. Thinly slice crosswise.
In a 10- to 12-inch frying pan over medium heat, melt butter. When it's foamy, add leek and stir until soft, about 5 minutes. Pour in cream, increase heat to medium-high, and stir often until liquid is reduced by about half, 3 to 4 minutes. Add salt and pepper to taste.
Add all the peas and half the mint and stir just until heated through, about 1 minute. Pour into a serving bowl and sprinkle with remaining mint.
How to Prepare Peas:
To shell fresh pea pods, break open the pods by pressing on one end - the pod should pop open at the seam. Then run your thumb down the opening to release the peas. One pound of peas in the pod yields approximately 1 cup of shelled peas.
To trim edible-pea pods, such as sugar snap and snow, cut or snap off ends and pull up sharply to remove any string on the pea. Discard ends and strings.
To blanch fresh peas (either shelled or whole edible-pod types), if the recipe calls for it, bring water to a boil in a large pan, then add peas. Cook just until they start to turn a brighter green, 15 to 30 seconds, then drain immediately. Rinse well under cold running water until cool, then drain again.