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1
Cut the florets from the broccoli stalks; cut the florets into pieces of about 1/2 inch.
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2
Trim the rough bottoms from the stalks, peel the stalks, and cut them into 1/2-inch dice.
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3
Heat the oil in a large pot over medium heat; add in the potatoes and cook, stirring, until they are golden and begin to stick to the bottom of the pot (don't worry if they stick; the little brown bits will add lots of flavor to the soup).
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4
Whack the garlic with the flat side of a knife, stir it into the pot and cook for a few minutes, stirring occasionally, until you can smell the garlic.
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5
Pour in the hot water and bring to a vigorous boil, stirring as you do to scrape up any browned bits of potato.
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6
Toss in the bay leaves and cook for 15 minutes.
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7
Stir in the lentils, decrease heat to simmering, and let simmer 15 minutes.
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8
Stir in the broccoli; season the soup with salt and pepper; cook until the broccoli and lentils are very tender, about 15 minutes.
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9
Skim any foam that rises to the surface as the soup simmers.
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10
Remove the soup from the heat; pluck out the bay leaves, and let the soup rest off the heat, 10-15 minutes.
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11
Ladle the soup into warm bowls and drizzle with olive oil; pass the grated Pecorino separately.
