I would seriously consider removing the concrete stoop altogether, and rebuilding using srw blocks (segmental retaining wall) like pisa or celtik block. No matter what you do with this concrete slab it will always look like an add on. If you decide to keep that slab then all you would need to do is use tapcons to adhere the wood to the concrete. Home depot has a good selection of galvanized brackets that will work fine. One end is tapconed to the concrete and the other is screwed in to the wood.
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