Step 1
Preheat oven to 300°. Toss squash and 1½ tsp. kosher salt in a colander; set over a bowl. Let sit 10 minutes, then pat dry with paper towels.
Step 2
Toss hazelnuts and 1 Tbsp. oil on a rimmed baking sheet and roast, shaking occasionally, until golden brown, 15–20 minutes. Let cool; crush into large pieces with a measuring cup or glass.
Step 3
Smack 3 mint sprigs against your cutting board a few times to release their flavor; mix in a large bowl with garlic, vinegar, sugar, red pepper flakes, and 2 Tbsp. oil; set dressing aside.
Step 4
Heat 2 Tbsp. oil in a large skillet, preferably cast iron, over medium-high until shimmering. Arrange squash cut side down in skillet, breaking into smaller pieces if needed in order to fit in a single layer, and cook, moving around in pan to ensure even browning, until golden brown on cut side, about 5 minutes. Reduce heat to medium-low, cover (if you don’t have a lid use a baking sheet), and continue to cook until very tender, about 15 minutes. Transfer to a cutting board and let cool slightly.
Step 5
Cut squash into 2″ pieces and toss in reserved dressing to coat; season with kosher salt and black pepper. Let sit at room temperature, tossing occasionally, 15 minutes. Pluck out mint sprigs; discard.
Step 6
Meanwhile, zest lemon half into a small bowl, mix in ricotta and remaining 1 Tbsp. oil; season with kosher salt. Hang on to that lemon.
Step 7
Spread lemon ricotta over platter. Top with squash and their juices. Squeeze reserved lemon over. Pull leaves from remaining mint sprigs (you want about ¼ cup). Scatter mint and hazelnuts over squash. Drizzle generously with oil and sprinkle with sea salt.
