Gently open each blossom and remove the pistils or stamen. Tear a single seam down each blossom to give clearance for the cashew cheese. Check for any bugs inside of the flowers and relocate them, if needed. Gently rinse the blossoms and lightly blot with a towel.
Fill a cake decorating funnel bag with the cashew cheese (or cut a corner off of a plastic freezer bag and use that to squeeze the cheese into the blossoms). Generously fill each blossom, making sure that each one gets enough cheese before pressing the blossoms closed with the sticky cashew cheese keeping them shut. Ideally you should use all of the cashew cheese mixture. (The flouring will also help encase the blossom, and so don't be afraid to be generous with the filling.)
Fill a small bowl with non-dairy milk and cornstarch. Stir until the cornstarch dissolves.
On a separate plate, combine the flour, oregano, thyme, salt, and pepper.
Before breading the flowers, cover the bottom of a pan with oil, about ¼ inch deep. Set it to a medium high heat and let it warm.
Dip each flower into the milk mixture, shake to remove excess, and roll in the flour. (Actually rolling the flowers through the flour will help set the cheese inside.) Set aside on a plate while you finish the rest of the flowers.
Put a pinch of flour in the pan, and if bubbles immediately form around it, the oil is hot and ready. Add the blossoms to the oil. Let them brown before turning, until each side is crisp and done. They will cook in about five minutes.
When the blossoms are done, move them to a paper towel or kitchen towel-lined plate to drain excess oil and then serve.