How to Make It
Whisk together flour, sugar, polenta, and 3/4 teaspoon salt in a medium bowl. Whisk together milk and eggs in a small bowl. Add milk mixture to flour mixture, and whisk until smooth. Cover and chill at least 2 hours or up to overnight (about 8 hours).
Preheat oven to 425°F with oven rack in lower third of oven. Remove batter from the refrigerator; whisk until well combined, and allow to stand at room temperature while oven preheats. Place a 10-inch cast-iron skillet in preheated oven, and let heat 15 minutes. Add butter pieces to skillet, and return to oven for 1 minute. Carefully remove skillet from oven, and swirl, if needed, until butter is completely melted and beginning to brown.
Whisk batter again until well combined. Working quickly, pour batter into skillet. Sprinkle ham and cheese around edges of batter, leaving about a 4-inch-wide circle in center. Immediately return skillet to oven, and bake until golden brown, puffed, and center is cooked through, 16 to 20 minutes.
While batter bakes, whisk together Dijon, vinegar, maple syrup, and remaining 1/8 teaspoon salt in a small bowl. Gradually add oil, whisking until dressing is emulsified. Toss arugula with 2 teaspoons of the dressing.
Carefully transfer hot Dutch baby to a serving plate. Serve immediately with dressed arugula and grapes, and drizzle with remaining dressing.