Place the potatoes in an even layer, cut side down, in a large skillet.
Add the water to the skillet along with the salt, butter, 2 dill sprigs, and garlic.
Cover the skillet and bring to a boil over medium/high heat. Cook for 15 minutes.
Uncover the skillet, remove the dill, and continue cooking the potatoes for an additional 10 minutes until the water evaporates and the potatoes sizzle in the butter remaining in the pan.
Check the potatoes occasionally to make sure they're not sticking, and continue browning the potatoes until deeply golden in color.
Turn off the heat.
Add the lemon zest, lemon juice and additional chopped dill if desired.
Stir, and serve immediately.