Bring a large pot of salted water to a boil. Make the dressing: Whisk the anchovies, grated garlic, vinegar and mustard in a large bowl. Slowly whisk in 3 tablespoons olive oil. Season with salt and pepper and set aside.
Combine the remaining 1/4 cup olive oil and the sliced garlic in a large skillet over medium-high heat. Cook, stirring occasionally, until the garlic is golden, about 2 minutes. Add the tomatoes, oregano, red pepper flakes and 1/2 teaspoon salt. Bring to a boil, then reduce the heat and simmer, stirring occasionally, until thickened, 10 to 12 minutes. Stir in the olives and capers.
Meanwhile, add the spaghetti to the boiling water and cook as the label directs for al dente. Reserve 1 cup cooking water, then drain the spaghetti and transfer to the skillet with the sauce. Add 1/2 cup of the reserved cooking water and cook, tossing, until well coated, 1 to 2 minutes, adding more cooking water as needed to loosen. Stir in the chopped parsley; season with salt and pepper.
Divide the spaghetti among bowls. Add the escarole and parsley leaves to the anchovy dressing; toss to coat. Pile the salad on top of the spaghetti.