Marinate chicken in enough EVOO to coat, the juice of 1 lemon, thyme, salt and pepper. Marinate about 1/2 hour.
Bring a large pot of water to a boil.
Using a small, sharp knife, core the Brussels sprouts and separate leaves. Salt water and add all of the baby cabbage leaves to pot you should have at least 6 cups loosely packed. Count to 30 then drain and cold shock the leaves; drain again.
Heat a grill pan and grill the chicken about 12 minutes, turning occasionally.
Combine the juice of remaining lemon, grated or pasted garlic, anchovy paste, Worcestershire, lots of black pepper and about 1/4 cup of EVOO to a bowl and whisk to make dressing. Add a small handful of cheese once dressing is emulsified. (I add a beaten egg yolk to our dressing with the lemon juice but there is a food safety risk with this addition, of course.)
Heat butter in small skillet with crushed garlic over medium heat, add breadcrumbs and toast to golden brown. Add parsley and remove garlic.
Toss Brussels greens with dressing. Serve on plates topped with sliced grilled chicken, more cheese and buttery breadcrumbs.