In Italian, the name for this custardlike dessert means "cooked cream."
Place cream and sugar in a medium saucepan. With a paring knife, split vanilla bean lengthwise; scrape out seeds, and add to cream along with empty pod (if using vanilla extract, add to yogurt mixture in step 4).
Bring cream to a boil, stirring to dissolve sugar. Cover pan, remove from heat, and set aside to steep, at least 10 minutes.
Meanwhile, place 1/2 cup cold water in a small bowl, and sprinkle gelatin over water; set aside to soften, at least 5 minutes. In a large bowl, whisk yogurt, honey, and salt until combined; set aside.
Return cream to a boil. Remove from heat, and immediately stir in softened gelatin until dissolved. Pour mixture through a fine-mesh sieve into yogurt-honey mixture; mix until combined.
Divide mixture among eight 4- to 6-ounce ramekins. Chill until firm, at least 4 hours and up to 2 days.
To serve, unmold each panna cotta from its ramekin: Run a paring knife around the top inner edge of ramekin, then dip bottom of ramekin in a bowl of boiling water for 10 seconds. Invert ramekin onto serving plate. Holding ramekin tightly to plate, shake firmly to release panna cotta. Drizzle with honey before serving.