In a small saucepan, place tomatoes in just enough water to cover. Bring to boiling. Reduce heat. Simmer about 2 minutes or until tender. Drain and finely chop. In a small mixing bowl, stir together cream cheese, Monterey Jack cheese, thyme, milk, and chopped tomatoes.
Brush one side of three tortillas with some of the cooking oil. Place tortillas, oil side down, on a large baking sheet. Spread tortillas with cream cheese mixture. Top with remaining tortillas. Brush the tops with remaining oil.