Alison Roman Shallot Anchovie Pasta

4 tbsp olive oil
6 large shallots, very thinly sliced
5 garlic cloves, 4 thinly sliced, 1 finely chopped
Salt and freshly ground black pepper
1 tsp red pepper flakes, plus more to taste
1 x 50g tin anchovy fillets (about 12), drained
8-12 tbsp tomato paste
280g pasta
Handful of parsley, leaves and tender stems, finely chopped
Sea salt flakes