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