Heat grill or grill pan to medium-high.
Fill a small skillet with about 1-inch water and bring to a boil.
Grate the garlic onto acutting board and add a couple teaspoons salt, mash into paste with the flat of your knife.
Add salt to boiling water and cook green beans 1 minute then drain and cool under cold running water then reserve.
Reserve 1/5 of the pasted garlic, about 1 clove and add the rest to a shallow dish. To the garlic, add the lemon zest, fennel seed, chopped thyme, rosemary, parsley and about 1/4 to 1/3 cup extra-virgin olive oil and some black pepper. Stir with a fork to combine then add chicken pieces and coat evenly. Grill chicken 12 to 15 minutes until juices run clear.
Bring a medium saucepan of water to a boil.
Trim asparagus of tough ends. Add salt and the asparagus to the water and blanch for 2 minutes. Remove from the water and place into an ice water bath to cool. Once cooled, pat dry with paper towels, drizzle with a touch of extra-virgin olive oil and season with salt and pepper. Divide the asparagus into 4 piles and roll 2 layered slices of prosciutto around each pile to form bundles. Grill 7 to 8 minutes until prosciutto is crisp and spears are tender.
Place basil and mint leaves in a food processor with the nuts. Add some salt and pepper and turn processor on. Stream in about 1/4 to 1/3 cup extra-virgin olive oil to form a thick pasty sauce. Transfer the sauce to a bowl. Stir in the reserved garlic paste and the grated cheese. Add the cooled green beans and the canned beans to the bowl and stir to combine. Adjust seasoning.
Remove chicken from the grill and squeeze the juice of 1 of the zested lemons down over the meat while still hot.
Serve 1 piece each chicken breast and thigh with an asparagus bundle and some bean salad alongside.