1½ lb. skinless, boneless chicken thighs
2 garlic cloves
3 oil-packed anchovy fillets (optional)
1 red chile (such as Fresno or Holland), seeds removed, coarsely chopped
2 Tbsp. tomato paste
2 tsp. finely chopped oregano
3 Tbsp. extra-virgin olive oil, plus more for grilling
2 lemons, halved
2 medium fennel bulbs, tough outer layers removed, halved lengthwise, thinly sliced crosswise
1 small white onion, very thinly sliced into rounds
2 Tbsp. unseasoned rice vinegar
2 Tbsp. extra-virgin olive oil
1 Tbsp. toasted white and/or black sesame seeds
Pat chicken dry and season with salt. Set aside on a plate.
Smash garlic under the flat side of a chef’s knife on your cutting board. Add anchovies, if using, chile, and a couple of pinches of salt and continue smashing with the side of your knife until a paste forms. (You can also do this with a mortar and pestle.) Transfer paste to a large bowl and stir in tomato paste, oregano, and 3 Tbsp. oil. Add chicken and toss to coat. Let sit at room temperature 1 hour.
Meanwhile, prepare a grill for medium heat. Clean and oil grate. Grill chicken, turning once, until lightly charred and cooked through, about 4 minutes per side.
While the chicken is cooking, grill lemons, cut side down, until lightly charred and starting to caramelize, about 4 minutes. Transfer to a platter.
Transfer chicken to platter with lemons and let rest 5 minutes.
While the chicken is resting, toss fennel, onion, and vinegar in a medium bowl; drizzle with oil and season with a big pinch of salt. Toss once more.
Mound fennel salad next to chicken and sprinkle sesame seeds over both. Squeeze grilled lemons over chicken and fennel salad.