Step 1

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).

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

Carefully transfer hot Dutch baby to a serving plate. Serve immediately with dressed arugula and grapes, and drizzle with remaining dressing.