A day before cooking, rinse the chicken inside and out under cold water and pat dry. Salt liberally, cover and refrigerate.
Remove the chicken from the refrigerator 1 hour before cooking.
Preheat the oven to 425 degrees F.
Lift the skin off each chicken breast and wedge 3 lemon slices and 1 bay leaf between the skin and each breast. Put the garlic, onion, thyme and remaining lemon slices in the cavity of the chicken. Rub the entire chicken liberally with the olive oil. Put the chicken in an ovenproof saute pan or roasting pan breast-side up, slide it into the oven and roast until the thigh reaches 160 degrees F, or until the cavity juices run clear, about 1 hour. Remove from the oven and let rest for 10 to 20 minutes.
When ready to serve, in a medium bowl, dress the arugula with the red wine vinegar and extra-virgin olive oil. Cut the chicken into 8 pieces, drizzle with the Salsa Verde and serve with the arugula salad.
Combine the extra-virgin olive oil, parsley, capers, mint, red pepper flakes, anchovies, garlic, lemon zest and juice, jalapeno and shallots in a bowl and stir to combine. Add salt and pepper to taste. Allow the flavors to meld for at least 15 minutes before serving; if planning to serve after more than an hour, add the lemon juice at the last minute to keep the color vibrant.