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1
Fill a medium bowl with water and squeeze the lemon half into it.
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2
Working with 1 artichoke at a time, snap off the dark outer leaves until you reach the yellow leaves.
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3
Cut off the top two-thirds of the leaves, leaving 1 1/2 inches at the base.
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4
Cut off the stem and peel the artichoke bottom, then scoop out the hairy choke with a melon baller or a teaspoon.
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5
Add the artichoke bottom to the bowl of water.
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6
Repeat with the remaining 3 artichokes.
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7
Scatter the diced carrot in a large saucepan and arrange the artichoke bottoms on top.
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8
Scatter the potato and peas around the artichokes and nestle the onion in the center.
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9
In a small bowl, whisk the olive oil with the flour, sugar and 1 tablespoon of the lemon juice.
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10
Stir in 1/4 cup of water and season with salt and pepper- Pour the mixture over the artichokes.
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11
Cover with a moistened piece of parchment paper and bring to a boil- Reduce the heat to moderately low and cook the vegetables until tender, about 1 hour.
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12
Check occasionally and add a few tablespoons of water as necessary if the vegetables begin to look dry.
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13
Transfer the artichoke bottoms to a smaller platter.
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14
Stir the dill and the remaining 1/2 tablespoon lemon juice into the vegetables in the pan and spoon them over the artichokes.
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15
Serve warm or at room temperature.
