Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper. Arrange the tomato slices on the baking sheet and sprinkle with brown sugar and cumin. Roast the tomatoes for 20 minutes, or until they are slightly shrivelled and caramelized.
Place the beets in a saucepan and cover them with cold water. Cover and bring to a boil. Cook for 40 minutes, or until the beets can be easily pierced with a fork. Drain the beets, and when cool enough to handle, peel and cut into chunks. In a food processor combine the beets, tahini, garlic, lime juice, and salt and purée.
In a medium bowl combine the parsley, grape tomatoes, onion, lime juice, salt, and pepper. Stir until mixed and set aside.
To assemble, toast the rye bread. Place a slice of toast on each plate.
Spread the Beet Tahini on the toast, top with a few Roasted Tomato Slices, a poached egg, and one tablespoon Parsley Salad. Sprinkle with sesame seeds and enjoy.