Step 1

Remove tough outer layers and fronds from fennel bulbs and discard. Working one at a time, cut bulbs lengthwise (through root ends) into quarters, remove cores, and slice quarters lengthwise into ½"-thick wedges.

Step 2

Heat oil in a large Dutch oven or other heavy pot over high until shimmering. Add fennel to pot, arranging in as even a layer as possible. Season with salt and cook, undisturbed, until golden brown underneath and starting to soften, 6–8 minutes. Using tongs, turn fennel over and cook until golden brown on the other side, 6–8 minutes.

Step 3

Reduce heat to low and add anchovies, garlic, red pepper flakes, and ½ cup mint to pot. Cook, stirring often, until anchovies are disintegrated and garlic is golden, about 2 minutes. Remove pot from heat and finely grate zest of orange and lemon directly into hot oil; stir well to evenly distribute. Cover pot to keep sauce warm and let sit until pasta is done.

Step 4

Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1½ cups pasta cooking liquid.

Step 5

Uncover sauce, add pasta and 1 cup reserved pasta cooking liquid, and set over medium-low heat. Add Pecorino and cook, tossing vigorously and adding more pasta cooking liquid if needed, until sauce is emulsified and pasta is coated, about 2 minutes.

Step 6

Divide pasta among bowls and top with torn mint.