Peel the guavas with a vegetable peeler. Cut them in half, crosswise and use a spoon to scoop out the center portions of the fruit to remove the seeds. Discard the seeds. Cut the guava into 1" -2" pieces.
In a large saucepan, combine the guava, sugar, water, vanilla seeds and vanilla bean as well as the cinnamon stick. Bring to a boil, then reduce heat and simmer on medium low for 15 minutes. Remove from heat and let the guava syrup steep for 20 minutes.
Place a large strainer over a large bowl and carefully pour the fruit and simple syrup into the strainer.
Discard the vanilla and cinnamon stick. Transfer the poached guava to the bowl of a food processor. Fasten the lid and pulse several times until you have a smooth puree.
Set a large sieve over a bowl and pour the puree into the sieve. Use the back of a spoon or a spatula to press the puree through the sieve. You should have about 1½ cups of guava puree. Cover and refrigerate.
FOR THE GUAVA SHERBET:
In a large saucepan, whisk together the milk, cream, guava simple syrup, corn syrup, sugar and kosher salt over medium heat. Continue whisking until the mixture almost comes to a simmer and the sugar is dissolved.
Transfer the milk mixture to a 4 cup liquid measuring cup with a spout or to a large pitcher. Set aside.
Create an ice bath in a large bowl with equal parts ice and water that fill the bowl halfway.
THIS TAKES TWO PEOPLE: Have one person hold a 1 quart zip-top FREEZER BAG open, gripping tightly to keep the bag upright. The other person carefully pours the milk mixture into the bag. Seal the bag completely and immerse it in the ice bath. Agitate the bag every 5 minutes or so to ensure that it's cooling evenly.
When most of the ice is melted in the ice bath and the milk mixture is cold, discard the ice water. Dry the bowl and pour the cold milk mixture into the bowl. Add the reserved guava puree and whisk until evenly combined. Cover and refrigerate at least 4 hours or overnight.
When you're ready to make the sherbet, pour the guava mixture into the ice cream maker and churn according to the manufacturers instructions. Transfer the sherbet to a container and cover with plastic wrap. Freeze until scoop-able, about 2 hours.
If you freeze the sherbet solid, let the sherbet sit out at room temperature for 5-10 minutes to soften slightly before scooping.