Preheat oven to 400 °F and position rack in the lower 3rd of your oven.
Wash and trim the roots and dark green tops of the leeks and discard the first two layers.
Slice the leeks in half length-wise. Rinse out any remaining dirt and pat dry.
In a baking sheet drizzle 2 Tbsp of olive oil. Roll leeks in the oil until evenly coated. Season all sides with salt and pepper to taste.
Arrange leeks on the baking sheet cut side down in a single layer. Roast for about 14-18 minutes or until the edges start to brown and the leeks soften.
Peel and smash 10 cloves of garlic.
In small sauce pan, over very low heat, combine garlic, 10 anchovy fillets, and 1/2 cup olive oil. Stir occasionally and mash the garlic with a fork once the garlic softens. The garlic and anchovies should be totally dispersed in the oil after about 12-14 minutes.
Finely chop 1/2 cup of walnuts. Add the walnuts and 2 Tbsp of butter to the sauce pan. Continue to cook the garlic, anchovies, and walnuts for 7-11 minutes until the walnuts are toasted.
To serve, top the roasted leeks with torn up pieces of burrata, walnut dressing, and fresh squeezed lemon juice along side crusty bread!
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