2 medium Idaho® potatoes, unpeeled, washed, rubbed clean and dry
4 cups extra-virgin olive oil, or enough to cover potatoes
2 tablespoons kosher salt
1/2 cup chicken stock or vegetable stock
1 pound trofie pasta (penne, gemelli or orecchiette may be substituted)
26 green beans, trimmed and washed
4 ounces crème fraîche
Kosher salt, to taste
Pinch coarse sea salt
1/2 pound fresh basil leaves
3 cloves garlic
1/2 cup extra-virgin olive oil
1/4 cup pine nuts or blanched almonds (optional)
1 lemon, zested and then juiced
1 1/2 teaspoons kosher salt
1/4 teaspoon cayenne pepper
1/4 cup freshly grated Parmigiano-Reggiano cheese
Put potatoes in heavy-bottomed pan; add enough olive oil to cover potatoes. Heat oil to just below a simmer, about 200ºF. (Do not let oil reach a higher temperature or potato jackets will be too crisp.) Cook potatoes 45 minutes to 1 hour, until tender with a slight resistance when pierced with sharp knife. (Potatoes will continue to cook after they are removed from heat.) Remove from heat, leaving potatoes in the oil. Let stand at least 1 hour, or refrigerate up to 24 hours.
Bring 4 quarts water to boil with 2 tablespoons kosher salt; stir in pasta. Cook until pasta is tender but not soft. Drain and reserve refrigerated, up to 1 day.
Blanch green beans in salted boiling water until just tender, 1 to 3 minutes. Drain and plunge into ice water to stop cooking, 1 to 2 minutes. Drain; cut into 1-inch pieces. Reserve refrigerated, up to 1 day.
Prepare Pesto: In food processor, combine basil and garlic until finely chopped. Scrape down bowl once; run for an additional minute. With motor running, add oil, nuts if using, lemon zest, lemon juice, salt and cayenne pepper. Scrape down bowl; process 30 seconds more, adding more oil if necessary to smooth out texture, and more lemon if desired.
Place Parmigiano-Reggiano in bowl; add basil mixture; stir to combine. Adjust seasoning to taste. Reserve refrigerated, up to 1 day.
For service, reheat potatoes in olive oil to 200ºF.
In heavy-bottomed sauté pan large enough to hold all the pasta, warm stock at medium heat. Add pasta; cook until most of stock absorbs into pasta, 3 to 4 minutes.
Add green beans and crème fraîche; increase heat to medium high; cook to a sauce-like consistency, 2 to 4 minutes. Taste for desired doneness of pasta and beans and add a bit more stock or water if necessary.
Reduce heat to medium; add half of the pesto and kosher salt to taste. Mix well; remove from heat.
Divide pasta mixture among 4 pasta bowls or plates. Carefully remove potatoes from oil; drain on paper towel. Cut potatoes in half and crumble one piece over each portion of pasta. Season potatoes with a pinch of sea salt and serve at once.