Make the garlicky tahini drizzle. In a medium bowl, combine the tahini, grated garlic, salt, pepper, sherry vinegar, and water. Whisk this mixture together until combined. Set aside.
Place a large sauté pan over medium heat. Add the sliced almonds to the pan. Toast the almonds, stirring around often, until deep brown on all sides, about 4-5 minutes. Transfer the almonds to a small plate and set aside. Return the pan to the heat.
Pour the olive oil into the pan and swirl it around. Add the cauliflower to the pan and spread it out into a single layer. Season with salt and pepper. Let it sit until it browns a bit on one side, about 4 minutes. Then, give the cauliflower a stir, flipping the pieces over. Let the other side of the cauliflower brown for another 3 minutes.
Make a little space in the middle of the pan. If the pan seems dry, pour some more olive oil into that space. Add the thyme and smoked paprika to the oil (they will sizzle!) and stir to incorporate.
Add the green beans to the pan and stir. Season again with salt and pepper. Keep sautéing the vegetables, stirring occasionally, until the edges of the cauliflower are softened and the green beans are bright green and crisp-tender, about 6 more minutes. If you have some excessive browning happening on the bottom of the pan, just add some tiny splashes of water as you go and stir.
Once the vegetables are cooked, stir in the sherry vinegar. Turn off the heat and stir in the lemon zest. Transfer the sautéed cauliflower and green beans to your serving plate. Drizzle the top with the garlicky tahini. Finish with the toasted sliced almonds and chopped olives.