This looks like field bindweed. It can be difficult to control because of its deep roots and extensive underground stems. Hand removal as soon as the plant shows up, trying to get all the plant parts as possible with deep cultivation and persistence can help. It will be difficult to control with an herbicide because there is not much labeled for use in vegetable gardens. Products that still have glyphosate as an active ingredient could be used, but care must be taken to only apply it to the weed and avoid drift, thus spot spraying with something to shield the spray is important. Persistence is the key here with repeated cultivation and/or herbicide applications.