Remove the pizza dough from the refrigerator and allow to sit at room temperature for 30 minutes.
Meanwhile, preheat the oven to 375 degrees F with a rack set in the middle position.
Break apart the head of garlic to expose the individual cloves (leaving their skins intact), about 10 cloves total. Put the cloves onto a small baking sheet and toss with 1 teaspoon of the olive oil and a sprinkle of salt and pepper. Bake, turning the cloves over halfway through the cooking time, until very tender, 12 to 15 minutes. Allow to cool slightly.
Set a 2-burner cast-iron grill pan over medium-high heat.
Once cool enough to handle, remove the skins from the garlic cloves and use the back of a knife to mash the cloves on a cutting board. Transfer the mashed garlic to a large bowl and add the ricotta cheese, Parmesan cheese, 4 tablespoons of the olive oil and the oregano. Stir to combine and season to taste with salt and pepper. Reserve.
Divide the dough in half and lightly dust a clean work surface with flour. Stretch and/or roll each piece into an 8-by-13-inch rectangle, about 1/8 inch thick. Lightly oil the grill pan. Working with 1 rolled dough piece, grill the crust until it starts to puff and distinct grill marks appear, 2 to 4 minutes. Use a pair of tongs to flip the crust and brush the edges of the dough with 1 teaspoon of olive oil. Grill until the the dough is just cooked through and distinct grill marks appear on the second side, about 2 minutes. Remove to a baking sheet. Repeat with second piece of dough
Turn the oven up to 400 degrees F.
Evenly spread the ricotta cheese mixture between the 2 crusts. Sprinkle the mozzarella and fontina cheese on each pizza crust. Bake until the cheese is melted, about 10 minutes.
Dress the kale or frisee with lemon juice, olive oil and salt and pepper and top the pizza. Cut each pizza into 8 pieces and serve immediately.