To proof the yeast, mix together warm milk, sugar, yeast, and water in a big basin. Until the mixture starts to foam and bubble, which should take around 5 to 10 minutes, set it aside. Doing so awakens the yeast, which is essential for perfectly rising focaccia.
To make the dough, combine the yeast mixture with around 560g of flour, ⅔ cup of vegetable oil, and a pinch of salt. Mix until a crumbly dough is formed. Add the rest of the flour little by little until a soft dough forms and pulls away from bowl edges.
After dusting a surface with flour, transfer the dough and knead it for 10 minutes, or until it becomes elastic and smooth. An alternative would be to use a dough hook attachment on a stand mixer.
First Rise: In a big basin that has been lightly greased, put the dough. Place it in a warm spot and cover it with plastic wrap or a moist towel. Allow it to rise for one to two hours, or until it has doubled in size.
Preheat the oven to 200°C (400°F) while the dough is rising. Then, roast the vegetables. On a baking sheet, distribute the red bell pepper bits that you just chopped. Season with salt and pepper, then roast in a drizzle of olive oil for 20-25 minutes, or until softened and gently browned.
To make the topping, mix together the paprika, lemon zest, olive oil, and minced garlic in a small bowl. Remove from the heat.
Punch down the dough gently to remove the air bubbles after it has doubled in size. Then, proceed to the second rise and dimple the dough. Place it in an oiled baking dish. Indent the dough all over with your fingers to make dimples.