In a large bowl, whisk together sugar and gelatin.

In a small saucepan, heat 1 1/2 cups half-and-half over medium-low until it starts to simmer.

Add to the bowl and whisk constantly until sugar and gelatin completely dissolve (2 to 3 minutes).

Add the remaining 2 1/2 cups half-and-half, yogurt, vanilla extract, and salt.

Scrape in the seeds from the vanilla bean and whisk until blended.

Pour the mixture into a 12-cup gelatin ring mold with a simple pattern and refrigerate until set, about 6 hours.

Toss 2 lb strawberries and 1/2 cup sugar in a large bowl.

Let stand at room temperature until berries soften and release juices, about 2 hours.

Strain the berries over a large bowl using a fine-mesh strainer.

Add the berries to a large saucepan and reserve the juices.

Add the remaining 1 lb strawberries and 3 cups water to the saucepan.

Bring to a low simmer and cook until the syrup is deep red and berries have lost color (about 20 minutes).

Strain the syrup into a medium bowl and discard the berries.

Add the reserved juices to the saucepan.

Bring the syrup to a simmer over low heat.

In a large bowl, whisk together the remaining 1 1/2 cups sugar and gelatin.

Whisk in the hot syrup until completely dissolved (1 to 2 minutes).

Let cool to room temperature.

Fill a sink with about 1 inch of lukewarm water.

Place the mold in the sink until the panna cotta loosens, then gently loosen it from the sides and bottom of the mold.

Pour the strawberry syrup down the sides and center of the mold so it flows underneath the panna cotta.

Refrigerate until completely set, at least 4 hours.

Fill a sink with about 1 inch of lukewarm water.

Place the mold in the sink until the gelatin loosens, then gently loosen it from the sides.

Invert the gelatin onto a platter and cut into slices.