Take the pieces of jackfruit and cut off the hard, triangular part at the bottom of each one. Slice the removed hard pieces into small, thin pieces.
Add all of the jackfruit to a medium mixing bowl. Add the poultry seasoning, salt, and pepper add toss until the jackfruit is well coated.
Heat a skillet to medium and drizzle with oil (or add a small amount of broth or water to the skillet if avoiding oil). Add the onion and sauté for 1 minute. Next add the rosemary and garlic to the skillet and sauté 1 more minute.
Add the jackfruit to the skillet. Sauté, stirring occasionally, until onion is transluscent and the jackfruit is browned.
Add the broth to the skillet and bring it to a bowl. Once boiling, cover with a lid and turn the heat down to low to medium-low, just enough to keep a light simmer. Keep at a light simmer for 15 minutes.
Remove the lid from the skillet, add the cherry tomatoes, replace the lid, and continue to simmer for another 10 minutes.
While jackfruit simmers, whisk together the non-dairy milk and the cornstarch.
When the 10 minutes has passed, remove the lid, and using two forks, shred the jackfruit pieces. If some pieces are hard or unshreddable, smash them using the back of a fork.
Turn the heat back to medium. Whisk the milk/cornstarch mixture in with the jackfruit. Next, stir in the spinach. Cook until spinach is wilted and sauce has thickened. Add salt and pepper to taste. Serve over cooked rice or starch of choice.