Combine flour, yeast, salt, and sugar in a big bowl. Mix with a spoon.
Add water, a little bit at a time; then add milk and 1 Tbsp of extra-virgin olive oil. Mix until combined and then start kneading, until soft. (Keep in mind that the dough should be very soft but manageable. If needed, add a bit more flour until the dough no longer sticks to your fingers).
Cover the bowl with a towel and let the dough rest in a warm place for about 2 hours.
Brush a baking sheet with olive oil and transfer the dough on it. Shape the dough into an oval, and using your fingers, press straight down to create deep dimples. Let it rest in a warm place for 30 more minutes.
Trim off the bottom stem of the radicchio and separate the leaves. Quickly sautee radicchio in a pan with a drizzle of oil and a sprinkle of salt, for 2 to 5 minutes, depending on the type of radicchio you are using. The key is sauteeing it quickly, softening it while maintaining a bit of crunch. Remove from the heat and set aside.
Turn the oven to 180 C (360 F).
In a small bowl, combine 3 Tbsp of Extra-virgin olive oil with 1 Tbsp of water. Brush the top of the dough with this solution, making sure you are using it all. Sprinkle with coarse sea salt.
Bake dough for 15 minutes. Remove the focaccia from the oven, spread the cooked radicchio on top. Place focaccia back in the oven and bake for 20-25 more minutes, until lightly golden brown.
Remove focaccia from the oven. Arrange a few speck slices on top of it and sprinkle small pieces of burrata all over it. Serve while it's still warm.
Recipe by Very EATalian