Place cut potatoes into a large saucepan and cover with water. Bring to a boil over high heat, reduce heat to medium-low, cover, and simmer until potatoes are tender when pierced with a knife, about 15 minutes. Drain potatoes and place into a large bowl, set aside to cool.
Place asparagus in a steamer rack over boiling water, cover the steamer, and cook until tender and crisp, about 3 minutes. Remove the rack from the pan and rinse asparagus under cold water until cool. Pat dry and set aside.
In a small bowl whisk together garlic, lemon zest, lemon juice, mustard, honey, olive oil, salt, and pepper.
Add the asparagus, peas, dill, basil, parsley to the potatoes. Pour the dressing over potato salad and mix. Serve immediately or refrigerate.
Store in a airtight container in the refrigerator for 3 to 4 days.