Preheat the oven to 425°F. Measure out just ¼ cup flour and set it aside. In a large bowl, add the remaining 1 cup flour, ½ cup cold water, 2 tbsp olive oil, and ¼ tsp salt. Mix until well combined with a spoon. Place the dough on a clean workspace. Knead the dough by pressing it down and folding it repeatedly until it’s a smooth ball. Wrap the dough in plastic wrap and place in the refrigerator.
Destem the kale and thinly chop the leaves. Halve the grape tomatoes. Thinly slice the cucumber into rounds. Drain and roughly chop the artichoke hearts, then dry them with a paper towel.
Place a large nonstick skillet over medium-high heat and add the butter. Once melted, add the artichoke hearts and cook until crisp in places, about 3 to 4 minutes. Add the kale and grape tomatoes and cook until the kale is wilted, about 2 to 3 minutes. Add the hot sauce and stir to combine. Taste, adjust seasoning with salt, and remove from the heat.
Lightly dust a clean workspace with 1 tbsp of the reserved flour. Using a rolling pin, roll the dough into a round about an ⅛ inch thick and 12 inches in diameter. Use the remaining flour to keep the dough from sticking (add more flour as necessary). Spoon the filling onto one side of the dough, 1 inch from the edge. Fold the dough over to close. Use a fork or your fingers to press the two sides together at the seam.
Carefully transfer the calzone to a baking sheet with your hands. Drizzle with 1 tsp olive oil, rubbing it over the top with your fingers or a brush, and cut a few small holes into the dough. Bake the calzones until the dough is cooked through and is lightly browned on top, about 15 to 18 minutes.
In a large bowl, whisk together the red wine vinegar, Dijon mustard, 1 tbsp olive oil, and a pinch of salt and pepper. Once the calzone is ready, toss half the spring mix (reserving half for the Chickpea Stuffed Avocado recipe) and sliced cucumber with the dressing in the large bowl. Cut the Buffalo artichoke calzone into slices and serve with the spring greens salad and bleu cheese dressing on the side.