Salt and pepper the fish and dredge in flour. Shake off excess.
In a heavy saucepan saute the onion in 2 Tbs. Olive oil. When translucent, add the garlic and slowly saute another minute. Stir in 2 tablespoons flour, blend well, and cook, stirring for a minute or two. Off heat pour in the wine and boiling water; whisk thoroughly. Return to heat, whisking as the sauce thickens. Add bay leaves, thyme, and tomato puree. Let simmer while you sear the fish.
In a pan large enough to hold the 4 walleyes in one layer, heat the remaining oil and when hot, but nor smoking, sear the fish quickly on each side.
Now, pour the red wine sauce over the fish. Bring to a boil, then quickly lower the heat. Cover and let simmer for about 15 minutes.
Just before serving remove the bay leaves, adjust the seasoning (the sauce will probably need salt and pepper), toss the capers in, and sprinkle with chopped parsley on top.