In a deep, medium skillet, bring the chicken broth and 1 cup water to a boil. Reduce the heat to a simmer and add the bay leaf. Using a 10-inch-long piece of kitchen string, tie the rosemary, thyme and parsley stems into a bundle. Tie the end of the string to the skillet handle and drop the herbs into the broth. Add the chicken and carrot and simmer over medium heat until the chicken is cooked through and the carrots are tender, about 15 minutes. Discard the herb bundle and bay leaf.
Reserve a ladle of broth and, using a slotted spoon, transfer the chicken and carrots to a bowl and let cool for a few minutes. Transfer the chicken mixture to a food processor along with the reserved broth and pulse to form a pate-like consistency. Serve on toast points.