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Step 1
Fill a large bowl with water; halve and squeeze 2 lemons into it.
Step 2
If using large artichokes: Clean them down to the hearts, following the guidelines shown here. If using small artichokes: Trim artichokes following Roman-Jewish artichoke guidelines shown here. Transfer cleaned artichokes to bowl of lemon water as you work, covering them with a clean kitchen towel to keep them completely submerged.
Step 3
In a 3-quart sauté pan or saucier, heat olive oil over medium heat until shimmering. Add onion, carrot, and garlic, and cook, stirring frequently, until just starting to soften, about 4 minutes. Nestle cleaned artichokes and their stems on top, then add white wine and bring to a simmer; lower heat to maintain a gentle simmer and cook for 4 minutes.
Step 4
Add stock, season lightly with salt, and return to a simmer. Add herbs. Cover and cook at a gentle simmer until artichokes and other vegetables are tender enough to easily slide a fork through them, about 25 minutes (cooking time will vary depending on the age and size of artichokes; if liquid level ever gets too low, add a little more water).
Step 5
Discard herb bundle. Using a slotted spoon, transfer artichokes, onions, carrots, and garlic, to a serving plate and keep warm. Return cooking liquid to the heat and simmer until slightly syrupy and reduced to about 3/4 cup (175ml).
Step 6
Whisk in butter and minced parsley, season with salt and pepper, then pour sauce over warmed platter of vegetables. Serve warm or at room temperature.