If you wait long enough we all die, so using "death" as a binary marker doesn't really make much sense in survival analysis. One might make an argument that "recurrence" would be OK as a binary marker, but then you're throwing out information about time to recurrence.
survivalROC package in R, as you note, will do what you want for a specified
predict.time. To work with censored data there has to be some smoothing to ensure a monotonic ROC, so you have to specify the method and parameter values for the smoothing. I found it easiest to specify a
span value, effectively the fraction of the data, ranked ordered by the predictor, over which smoothing is done. Read the paper to understand the details.
Recognize, however, that a ROC does not represent the most appropriate way to evaluate or use a survival model. This Cross Validated page provides a good entry into discussion of alternatives.
In response to paragraph added in revised question
Your proposed use of an ROC curve to choose treatments of patients based on results of a single test is problematic in several ways.
First, if "The only factor significantly influencing OS and RFS is the variable/test I want to investigate," then you have a data sample whose results might be difficult to generalize to a different set of patients. Studies typically find relations of multiple clinical variables to overall survival (OS) or tumor recurrence-free survival (RFS). Such variables include age, smoking history, tumor grade, and cancer staging. If you found that none of these was "significantly influencing OS and RFS," then you seem to have had a very small data set or one that was otherwise restricted, for example a relatively homogeneous sample with respect to these clinically important variables.
Second, your focus on a single "significant" variable is extremely poor practice for prognostication. For prognostication you should not remove a variable from consideration just because it failed a test of statistical significance in a particular data set. This issue has been discussed extensively on this site, for example here.
Third, choosing an "optimal cut-off value" is fraught with danger, even if you move from your single-test result to a more realistic predictor combining multiple prognostic variables. Presumably there is some cost or danger to the proposed treatment for those at high risk, or it would be offered to all regardless of risk. What is the cost-benefit tradeoff, both from the clinician's and from the patient's perspective? As @FrankHarrell has put it, "ROC curves are not informative in 99% of the cases I've seen over the past few years." What you need is a way to estimate risk for a patient, in a way that can be combined with other clinical, personal, and practical considerations to inform a choice of treatment. A simple yes/no classification based on an "optimal cut-off value" does not accomplish this.
Fourth, your wish to use "recurrence" or "death" as binary variables without respect to time only makes sense in limited circumstances, and throws out all of the useful information about time to recurrence or death. Maybe you could consider this if you had essentially complete follow-up data on all patients up through a time by which, based on prior knowledge about this disease, almost all recurrences or disease-related deaths are likely to occur. But that's not often the case in cancer. Even in that case, why not use the tools provided by survival analysis to learn from all the information that you have?
You will be much better off moving away from your ROC curves toward the more complete survival modeling provided by tools like those in the
rms package in R. These tools can be used to calibrate and validate your survival model and to produce nomograms that combine multiple variables for prognostication. Links from this answer provide related resources.