Honey-Soy Glazed Tofu with Carrot-Ginger Sauce

(1 1/2-2-inch) knob freshly peeled ginger

Carrots

Garlic clove

Sesame seeds and sliced green onion

drained and pressed, and cut into slices 1 (14-oz.) block extra-firm tofu, extra-firm

Honey

Soy sauce or tamari, reduced-sodium

Neutral vegetable or canola oil

Rice vinegar

Sesame oil