For the gnocchi:

1. Bring milk, salt, and pepper to a high simmer, almost to a boil. Using a hand-held sifter, sift in semolina and whisk while doing so.
2. This prevents clumping and promotes even cooking of the semolina. Once all is incorporated, continue to cook briefly until starch is cooked through (it will begin to pull away from the pot and won’t be starchy in the mouth).
3. Turn off heat, beat in 1 egg at a time, fold in cheese at the end. Pour into an 8 x 8  baking dish sprayed with nonstick spray and press into an even layer. Cool in the refrigerator. When cool, cut it into inch by inch squares.

For the pesto:

1. Combine all ingredients in a food processor.
2. Pulse to combine.

To finish:

1. Warm a pot of oil to 350 degrees and fry gnocchi until they are golden brown, and then lift with a slotted strainer onto some paper towels to dry, adding salt and pepper.
2. In a bowl, add 2 tablespoons pesto and toss gnocchi, salt, extra parm, and a touch of EVOO. Serve immediately.