Preheat the oven to 400°F. Peel and chop the carrots. Thinly slice the fingerling potatoes. Add the carrots and parsnips to one side of a baking sheet and the sliced potatoes to the other. Toss everything with 2 tsp olive oil and a pinch of salt and pepper, keeping the potatoes separate. Sprinkle the dried oregano onto the potatoes. Roast until all the vegetables are browned in places and tender, about 20 to 25 minutes.
In a medium bowl, combine the garbanzo bean flour and 1 cup water and whisk well. Grate in 1 clove garlic with a microplane. Add 1 tbsp olive oil and ⅛ tsp salt. Whisk batter again to combine. Roughly chop the kalamata olives. Thinly slice the radish. Set the olives and radish aside.
Set the oven to broil on high. Place a large oven-safe nonstick skillet over medium-high heat with 2 tsp olive oil. Once hot, whisk the batter again, add to the hot skillet, and tilt to cover the bottom of the pan. Cook, undisturbed, until the socca begins to bubble, about 4 to 5 minutes. Transfer the skillet to the oven and broil the socca crust until browned on the edges, about 4 to 6 minutes. Remove from the oven.
Halve the lemon. Drain and rinse the cannellini beans. Add half of the beans (saving the rest for the Jackfruit Tacos Al Pastor), roasted carrots and parsnips, tahini, ½ tsp salt, and 2 tbsp lemon juice to a food processor. Blend on high to combine. With the motor running, drizzle in 2 tbsp olive oil and blend until smooth. Taste the carrot parsnip hummus and adjust seasoning with salt.
Spread the carrot parsnip hummus over the socca crust and top with the roasted fingerling potatoes and chopped olives.
In a large bowl combine the mizuna, sliced radish, any remaining lemon juice, and a pinch of salt and pepper. Transfer the socca pizza to a cutting board and top with some of the mizuna salad. Cut into pieces, transfer to large plates, and serve any remaining salad on the side.