Preheat oven to 375 degrees F (190 degrees C).
Meanwhile, give the Purple Carrot (5) a good scrub and rinse (no need to peel) and cut into quarters length-wise. Toss with Extra-Virgin Olive Oil (1 teaspoon) and a Salt and Pepper (to taste).
Lay the carrots flat onto a parchment-lined roasting sheet. Roast at 375 degrees F (190 degrees C) for 1 hour. The carrots should have softened yet still have some bite to them. Cooking time will depend on the size of the carrots and the strength of the oven.
For the garlic tahini, in a small bowl or food processor, whisk together Tahini (2 tablespoon), Lemon Juice (2 tablespoon), Garlic (1 clove), and a pinch of Kosher Salt (1 pinch).
Slowly add in the Water (4 tablespoon) a tablespoon at a time until the tahini loosely coats the back of the spoon. Measurements will inevitably vary for this.
For the carrot top oil, trim the green tops from the carrots and add them to a mortar and pestle. Bash them vigorously until they form a chunky paste.
Pour in Olive Oil (1/8 cup) and stir thoroughly to combine. Allow the mixture to sit for 1 hour at room temperature.
Line a mason jar with cheesecloth. Wrap an elastic band around the top of the jar to secure the cloth in place. Spoon the oil mixture overtop of the cloth.
Using the spoon, gently press the oil through the cheesecloth until all of the oil has passed through to the bottom of the jar. You should be left with slightly green oil that has an earthy yet mild carrot flavour.
Store in a sealed mason jar in the refrigerator for up to two weeks. Remove from fridge before using, allow it to come to room temperature and use it to flavour various dishes.
Dollop or smear the Garlic Tahini onto a serving platter. Arrange the roasted carrots overtop and drizzle with Carrot-Top oil. Garnish with Black and White Sesame Seeds (to taste).