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1
Slice each clove of garlic as thin as possible-aim for 1/8-inch to 1/4-inch-then cut each clove-worth of slices in half, so you end up with a bunch of thin half-moons.
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2
Set a heavy, non-reactive pan over a medium-low flame and add 2 tablespoons of butter. Let it just melt, and add the garlic. Keep the heat low-we don't want the garlic to brown. Stir frequently with a wooden spoon until the garlic has softened and is just beginning to go translucent, turning the heat down if needed, about 2 minutes.
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3
Add the finely chopped tomatoes and the remaining 1 tablespoon of butter. Let everything come to a bubbling simmer, stirring to mix here and there. Keep at a bubbling simmer until the tomato sauce is slightly darker in color, and has thickened-about 10 minutes or so. If the sauce is still looking a little thin, let simmer for an extra few minutes. (I usually like to boil my pasta while the sauce cooks.)
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4
Meanwhile, take a few basil leaves at a time, roll them, and slice into ribbons about 1/4-inch thick.
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5
When the pasta is done, add 1 teaspoon of kosher salt to the sauce, taste, then add more as needed (I sometimes like to add another big pinch).
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6
Remove the sauce from heat, stir in the basil, the pasta, the Parmigiano-Reggiano, and serve. To serve, add a good-size swoosh of ricotta onto the plate, then add the bucatini marinara on top, and sprinkle with more Parmigiano-Reggiano.
