While the chicken is roasting, place a large pot of water over high heat to boil the pasta. When the chicken has about 10 minutes left to cook, season the boiling water with salt and drop the pasta. Cook to al dente according to package directions. Save a couple of mugs full of starchy cooking water before draining the pasta. Reserve.
While the pasta is boiling, place a large skillet over medium-high heat with 2 turns of the pan of EVOO. Add the scallion whites and chopped garlic to the pan and cook until tender, about 2 minutes.
Add one mug full of the reserved pasta-cooking water and the cooked pasta to the pan and bring up to a bubble.
While that's heating up, place the egg yolks into a bowl and whisk to break them up. Add remaining cooking water to the egg yolks while whisking constantly to heat them up. Reduce the heat under the skillet to medium and add the egg mixture to the pasta, stirring constantly to incorporate. Add the tangerine juice, Parmigiano Reggiano, some salt and pepper to the pan, and simmer until thickened, about 2 minutes. Reserve warm.
When the chicken is done roasting, remove it from the oven and crank up the broiler. Pour the glaze over the chicken and pop it under the broiler to caramelize the glaze.
Garnish the pasta with the scallion greens and arugula and serve alongside the chicken.