Add tomato sauce, diced tomatoes, tomato paste, garlic, and herbs to slow cooker. Stir until well-combined.
Set chicken breasts on top of the sauce, sprinkle generously with salt and pepper, cover and cook on low for 6 hours (or on high for 3-4).
When done, use two forks to shred the chicken, or throw the breasts into the bowl of your stand mixer and use the paddle attachment to shred (I love this way so, so much!)
Slice the rolls in half and toast on a hot skillet.
Use tongs or a slotted spoon, tapping excess sauce into the pot, and place a generous helping of the chicken mixture into each of the sliced rolls.
Top with a generous sprinkling of grated Parmesan, mozzarella*, and avocado slices and serve.
Notes
*If you want to melt the cheese, put it under the broiler for a minute or two.