Slice an X into the bottom of each tomato with a paring knife. Lower tomatoes into a pot of boiling water and blanch for 15 to 30 seconds. Use a slotted spoon or a spider to remove the tomatoes from the pot. Immediately plunge into an ice-water bath until cool enough to handle, about 30 seconds. Then pull off each peel, gripping the skin between your thumb and the flat part of the knife blade, starting at the X. Using the tip of your knife, remove cores. Tear beefsteak tomatoes into pieces.
Heat oil and garlic, in a medium pot over medium heat until fragrant and sizzling, but not brown. Add tomatoes and season with salt, black pepper, and red-pepper flakes. Bring to a boil over high heat, then reduce to a rapid simmer and cook until tomatoes are falling apart and are reduced slightly, about 15 minutes.
Working in batches, pass through a food mill fitted with the fine disk into a bowl, or puree in a food processor, straining out seeds if desired. If not serving immediately, let cool completely and store in an airtight container it the refrigerator up to 3 days, or the freezer for 3 months.
Makes about 4 cups