Core and quarter tomatoes; if they are large cut them into 6th's or 8th's. You do not want them to be taller than your food dehydrator tray. Place cut tomatoes into a large bowl. You can choose whether to seed the tomatoes or not, I do not notice any added bitterness from the seeds. The moisture surrounding the seeds concentrates into a much deeper flavor profile so I choose to keep the tomato intact.
In a small microwave safe bowl, combine olive oil and smashed garlic. (See notes for how to smash garlic)
Cover bowl with a paper towel and microwave on high for 15-30 seconds. Oil should be warm, not boiling. Remove your garlic infused olive oil from the microwave and allow it to cool slightly, just a few minutes. Remove the smashed garlic from the oil and add chopped fresh basil, dried rosemary and kosher salt. Stir to combine well.
Pour mixture in bowl over cut tomatoes. Toss gently with your hands or a spoon to combine without bruising the tomatoes. Your tomatoes will be generously coated in the olive oil mixture. You could serve them over a bed of spring mix for a delightful salad at this point. The marinating tomatoes smell so good, the waiting is the hardest part.
Place marinated tomatoes in your food dehydrator tray so they are not touching. They will be very wet - you can shake off some of the liquid as you are taking them out of your prep bowl. Do not 'dry' them off or you will lose your depth of all these flavors.
I use a small 5-tray dehydrator and the entire batch fits nicely with a little room to spare. Plug in your food dehydrator and dry according to manufacturer's instructions. It takes roughly 10-15 hours to dehydrate tomatoes. I started mine in the afternoon and they were not all done by bed time, so I simply unplugged the dehydrator and then turned it back on in the morning.
Notes
To smash garlic: Lay the side of the blade of a chef´s knife (blade facing AWAY from you) on each clove and smash down with the heel of your palm, then remove peel.