Preheat oven to 375 degrees.
In a large bowl, toss the tomatoes and artichokes with olive oil, season with salt and oregano, and toss to combine. Arrange vegetables in a single layer on a sheet pan.
With a sharp knife, cut about 1/3 the top off a whole head of garlic (so all cloves are exposed). Drizzle with the remaining teaspoon of olive oil and wrap in a double layer of foil.
Place both the veggies and garlic on center rack of the oven. Roast tomatoes and artichokes until all tomatoes have burst, stirring once in the middle of roasting, 20-25 minutes.
Remove pan and allow veggies to cool. Continue roasting garlic for another 10 minutes, then remove from oven and open foil to cool.