Caramelize the onions and fennel: Heat olive oil in a large skillet with a tight-fitting lid over medium-high. Add the fennel and onion and season with salt and pepper. Cook, stirring occasionally until mixture begins to brown, about 5 minutes. Reduce heat to medium, cover, and cook 5-7 minutes. Uncover, add 1 Tbsp water and cook, stirring constantly, until golden brown and soft, about 2 minutes
Prepare pizza dough (optional; can be replaced with store bought dough): Pour 1 cup warm water into a medium bowl; add sugar and sprinkle with year and let stand until foamy, 5 minutes. Whisk oil and 1 tsp salt into yeast mixture. Add flour and stir with a wooden spoon until liquid is incorporated (dough will appear dry). Turn out onto a floured work surface. Knead until dough comes together in an elastic ball, 2 minutes. Transfer to an oiled medium bowl; brush lightly with oil. Cover bowl with plastic wrap; set in a warm, draft-free place until dough has doubled in bulk, 45 minutes. Punch down dough and cover; let rise another 30 minutes. Turn out dough into a lightly floured work surface. Divide into 4 equal pieces and let rest for 15 minutes before using.
Heat up a grill on medium-high heat.
On a foured surface, stretch the pizza dough into a 10-inch long oval or other desired shape. Brush one side lightly with olive oil and season with salt and pepper.
Place the dough, oiled side down, directly on the grill. Brush the top with olive oil and cook until underside is lightly charred and bubbles form all over top, 1 to 2 minutes. With tongs, flip dough and cook until lightly charred, 1 to 2 minutes. Slide dough to cooler side of grill.
Top with cheese and fennel fronds; cover grill. Cook until cheese melts and toppings are heated through, 2 to 5 minutes.