Step #1 Grate peel from lemon & reserve; you should have about 1 tbsp.
Step #2 Cut lemon in half & squeeze juice into a large bowl, discarding any seeds; fill bowl halfway with water.
Step #3 Break off artichokes' coarse green outer leaves down to tender yellow inner leaves (easily pierced with your fingernail).
Step #4 Cut off thorny tips & pare away fibrous green layers from bottoms.
Step #5 Cut each artichoke into quarters lengthwise; with a spoon, scoop out & discard fuzzy centers.
Step #6 Cut quarters into 1/2-inch wedges (if using baby artichokes, leave quarters whole).
Step #7 As you work, drop pieces into bowl with water & lemon juice.
Step #8 Drain artichokes.
Step #9 In a 10- to 12-inch nonstick frying pan over medium-high heat, & chili flakes until mixture is fragrant, grated lemon & orange peel, garlic, stir 2 tbsps olive oil, about 2 mins.
Step #11 Reduce heat to medium & pour in 1/2 c water; cover & cook this until water has been absorbed & artichokes are tender when pierced, about 15 mins.
Step #12 Remove from heat & stir in the vinegar & remaining 2 tbsps olive oil.
Step #13 Pour into a shallow bowl & let cool to about room temp.
Step #14 Before serving, stir in the parsley & add more salt to taste.