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1
Rinse the asparagus, and snap off the tough bottom stubs.
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2
Slice the spears crosswise into 1/3-inch chunks, including tips.
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3
Pour 1/3 cup of the olive oil into the pot, drop in the crushed garlic, and set over a medium-high flame.
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4
Golden the garlic for a minute or two, just until fragrant and lightly colored, and stir the potato cubes into the hot oil.
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5
Cook, stirring now and then, until the potatoes are crusty and starting to stick to the bottom but not brownedlower the heat if necessary4 or 5 minutes.
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6
Stir in the chopped leeks, and cook until softened and sizzling, 3 or 4 minutes more.
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7
Pour 5 quarts of water into the pot, drop in the bay leaves and tablespoon of salt, and stir well, scraping up any crusty potatoes on the bottom.
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8
Cover, and bring to the boil over high heat.
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9
Stir in all the cut asparagus, return to the boil, and adjust heat to keep the broth bubbling steadily and slowly reducing.
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10
Cook uncovered for about 1 1/2 hours, stirring occasionally, until the soup volume is reduced by almost a third and the broth is full of flavortasting is the way to test for doneness.
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11
Stir in the rice, return to the boil, and cook for 10 minutes, until the grains are al dente, then turn off the heat.
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12
Season with freshly ground black pepper, and more salt to taste.
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13
Stir in 2 tablespoons fresh olive oil and 1/2 cup grated cheese.
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14
Serve immediately in warm bowls, with more cheese and oil at the table.
